Unit: 3: Data Handling

Exercise: 3.1 (9)

 

Question: 1

Find the range of heights of any ten students of your class.

Solution

S.No.

Name of students

Height (in feet)

1.

Gunjan

4.2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiaac6 cacaaIYaaaaa@3804@

2.

Aditi

4.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiaac6 cacaaI1aaaaa@3807@

3.

Nikhil

5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaaaa@3697@

4.

Akhil

5.1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaiaac6 cacaaIXaaaaa@3804@

5.

Riya

5.2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaiaac6 cacaaIYaaaaa@3805@

6.

Akshat

5.3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaiaac6 cacaaIZaaaaa@3806@

7.

Abhishek

5.1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaiaac6 cacaaIXaaaaa@3804@

8.

Mayank

4.7 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiaac6 cacaaI3aaaaa@3809@

9.

Rahul

4.9 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiaac6 cacaaI5aaaaa@380B@

10.

Ayush

4.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaiaac6 cacaaI1aaaaa@3807@

Range=Highest heightLowest height Range=5.34.2 Range=1.1 =5.34.2=1.1 feet. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGsb Gaaeyyaiaab6gacaqGNbGaaeyzaiabg2da9iaabIeacaqGPbGaae4z aiaabIgacaqGLbGaae4CaiaabshacaqGGaGaaeiAaiaabwgacaqGPb Gaae4zaiaabIgacaqG0bGaeyOeI0Iaaeitaiaab+gacaqG3bGaaeyz aiaabohacaqG0bGaaeiiaiaabIgacaqGLbGaaeyAaiaabEgacaqGOb GaaeiDaaqaaiaabkfacaqGHbGaaeOBaiaabEgacaqGLbGaeyypa0Ja aeynaiaab6cacaqGZaGaeyOeI0Iaaeinaiaab6cacaqGYaaabaGaae OuaiaabggacaqGUbGaae4zaiaabwgacqGH9aqpcaqGXaGaaeOlaiaa bgdaaeaacqGH9aqpcaaI1aGaaiOlaiaaiodacqGHsislcaaI0aGaai OlaiaaikdacqGH9aqpcaaIXaGaaiOlaiaaigdacaqGGaGaaeOzaiaa bwgacaqGLbGaaeiDaiaab6caaaaa@7562@  

 

Question: 2

Organise the following marks in a class assessment, in a tabular form.

4

6

7

5

3

5

4

5

2

6

2

5

1

9

6

5

8

4

6

7

 

(i)              Which number is the highest?

(ii)           Which number is the lowest?

(iii)         What is the range of the data?

(iv)         Find the arithmetic mean.

Solution

S. No.

Marks

Tally marks

Frequency
(No. of students)

1

1

I

1

2

2

II

2

3

3

I

1

4

4

III

3

5

5

IIIII

5

6

6

IIII

4

7

7

II

2

8

8

I

1

9

9

I

1

 

(i)  The highest number is 9 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGyoaaaa@369B@ .

(ii)           The lowest number is 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaaaa@3693@ .

(iii)         The range of the data is 91=8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGyoaiabgk HiTiaaigdacqGH9aqpcaaI4aaaaa@3A0B@

(iv)         Arithmetic mean = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0daaa@36DE@

              4+6+7+5+3+5+4+5+2+6+2 +5+1+9+6+5+8+4+6+7 20 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaqaabe qaaiaaisdacqGHRaWkcaaI2aGaey4kaSIaaG4naiabgUcaRiaaiwda cqGHRaWkcaaIZaGaey4kaSIaaGynaiabgUcaRiaaisdacqGHRaWkca aI1aGaey4kaSIaaGOmaiabgUcaRiaaiAdacqGHRaWkcaaIYaaabaGa ey4kaSIaaGynaiabgUcaRiaaigdacqGHRaWkcaaI5aGaey4kaSIaaG OnaiabgUcaRiaaiwdacqGHRaWkcaaI4aGaey4kaSIaaGinaiabgUca RiaaiAdacqGHRaWkcaaI3aaaaeaacaaIYaGaaGimaaaaaaa@5717@

              = 100 20 =5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaGaaGimaiaaicdaaeaacaaIYaGaaGimaaaacqGH9aqp caaI1aaaaa@3C58@

Question: 3

Find the mean of the first five whole numbers.

Solution

The first five whole numbers are 0, 1, 2, 3 and 4. Therefore,

Mean of first five whole numbers

= Sum of numbers Total number MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa aeOBaiaabwhacaqGTbGaaeOyaiaabwgacaqGYbGaae4Caaqaaiaabs facaqGVbGaaeiDaiaabggacaqGSbGaaeiiaiaab6gacaqG1bGaaeyB aiaabkgacaqGLbGaaeOCaaaaaaa@4E2F@

= 0+1+2+3+4 5 = 10 5 =2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqGH9a qpdaWcaaqaaiaaicdacqGHRaWkcaaIXaGaey4kaSIaaGOmaiabgUca RiaaiodacqGHRaWkcaaI0aaabaGaaGynaaaaaeaacqGH9aqpdaWcaa qaaiaaigdacaaIWaaabaGaaGynaaaaaeaacqGH9aqpcaaIYaaaaaa@43F5@

Thus, the mean of first five whole numbers is 5.

Question: 4

A cricketer scores the following runs in eight innings:

58, 76, 40, 35, 46, 45, 0, 100.

Find the mean score.

Solution

Number of innings =8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ioaaaa@37A0@

Mean of score

= Sum of scores Number of innings MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa ae4CaiaabogacaqGVbGaaeOCaiaabwgacaqGZbaabaGaaeOtaiaabw hacaqGTbGaaeOyaiaabwgacaqGYbGaaeiiaiaab+gacaqGMbGaaeii aiaabMgacaqGUbGaaeOBaiaabMgacaqGUbGaae4zaiaabohaaaaaaa@5195@

= 58+76+40+35+46+45 + 0+100  8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI1aGaaGioaiabgUcaRiaaiEdacaaI2aGaey4kaSIaaGin aiaaicdacqGHRaWkcaaIZaGaaGynaiabgUcaRiaaisdacaaI2aGaey 4kaSIaaGinaiaaiwdacaGGGcGaey4kaSIaaiiOaiaaicdacqGHRaWk caaIXaGaaGimaiaaicdacaGGGcaabaGaaGioaaaaaaa@4D24@

= 400 8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI0aGaaGimaiaaicdaaeaacaaI4aaaaaaa@39E2@

=50 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ynaiaaicdaaaa@3857@

Thus, the mean score is 50.

Question: 5

Following table shows the points of each player scored in four games:

Player

Game
1

Game
2

Game
3

Game
4

A

14

16

10

10

B

0

8

6

4

C

8

11

Did not Play

13

 

Now answer the following questions:

(i)              Find the mean to determine A’s average number of points scored per game.

(ii)           To find the mean number of points per game for C, would you divide the total points by 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maaaa@3695@  or by 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGinaaaa@3696@ ? Why?

(iii)         B played in all the four games. How would you find the mean?

(iv)         Who is the best performer?

Solution

(i)              Average number of points of A

     = Sum of scores by A No. of games played by A   MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa ae4CaiaabogacaqGVbGaaeOCaiaabwgacaqGZbGaaeiOaiaabkgaca qG5bGaaeiiaiaabgeaaeaacaqGobGaae4Baiaab6cacaqGGaGaae4B aiaabAgacaqGGaGaae4zaiaabggacaqGTbGaaeyzaiaabohacaqGGa GaaeiCaiaabYgacaqGHbGaaeyEaiaabwgacaqGKbGaaeiiaiaabkga caqG5bGaaeiiaiaabgeaaaGaaeiiaaaa@5BCC@

          = 14+16+10+10 4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaGaaGinaiabgUcaRiaaigdacaaI2aGaey4kaSIaaGym aiaaicdacqGHRaWkcaaIXaGaaGimaaqaaiaaisdaaaaaaa@4030@  

          = 50 4   MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI1aGaaGimaaqaaiaaisdaaaGaaeiiaaaa@39C8@

          =12.5  MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaikdacaGGUaGaaGynaiaabccaaaa@3A69@

(ii)           We need to divide the total points by 3 as player C played only three games.

(iii)         Player B played in all the four games.

           Mean score of player B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyinIWLaae iiaiaab2eacaqGLbGaaeyyaiaab6gacaqGGaGaae4CaiaabogacaqG VbGaaeOCaiaabwgacaqGGaGaae4BaiaabAgacaqGGaGaaeiCaiaabY gacaqGHbGaaeyEaiaabwgacaqGYbGaaeiiaiaabkeaaaa@4ABC@

          = Sum of scores by B No. of games played by B MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa ae4CaiaabogacaqGVbGaaeOCaiaabwgacaqGZbGaaeiiaiaabkgaca qG5bGaaeiiaiaabkeaaeaacaqGobGaae4Baiaab6cacaqGGaGaae4B aiaabAgacaqGGaGaae4zaiaabggacaqGTbGaaeyzaiaabohacaqGGa GaaeiCaiaabYgacaqGHbGaaeyEaiaabwgacaqGKbGaaeiiaiaabkga caqG5bGaaeiiaiaabkeaaaaaaa@5AAB@

          = 0+8+6+4  4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIWaGaey4kaSIaaGioaiabgUcaRiaaiAdacqGHRaWkcaaI 0aGaaiiOaaqaaiaaisdaaaaaaa@3E70@

          = 18  4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaGaaGioaiaacckaaeaacaaI0aaaaaaa@3A4D@

          =4.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG inaiaac6cacaaI1aaaaa@390D@

(iv)         To find the best performer, we should know the mean of all the players played.

Mean score of player A=12.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeyqaiabg2 da9iaaigdacaaIYaGaaiOlaiaaiwdaaaa@3A8A@

          Mean score of player B=4.5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOqaiabg2 da9iaaisdacaGGUaGaaGynaaaa@39D2@

          Mean score of player C

          = 8+11+13 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI4aGaey4kaSIaaGymaiaaigdacqGHRaWkcaaIXaGaaG4m aaqaaiaaiodaaaaaaa@3D1F@

          = 32 3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIZaGaaGOmaaqaaiaaiodaaaaaaa@3924@

          =10.67 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaicdacaGGUaGaaGOnaiaaiEdaaaa@3A86@

Hence, on comparing mean scores of all the players, we found that player A is the best performer.

Question: 6

The marks (out of 100) obtained by a group of students in a science test are 85, 76, 90, 85, 39, 48, 56, 95, 81 and 75. Find the:

(i)              Highest and the lowest marks obtained by the students.

(ii)           Range of the marks obtained.

(iii)         Mean marks obtained by the group.

Solution

(i)              Highest marks obtained by the student =95 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG yoaiaaiwdaaaa@3860@

          Lowest marks obtained by the student =39 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4maiaaiMdaaaa@385E@

(ii)           Range of marks

          = MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0daaa@36DE@  Highest marks MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyOeI0caaa@36C5@  Lowest marks

          =9539=56 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG yoaiaaiwdacqGHsislcaaIZaGaaGyoaiabg2da9iaaiwdacaaI2aaa aa@3D52@

(iii)         Mean of obtained marks

          = Sum of marks Total number of marks MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa aeyBaiaabggacaqGYbGaae4AaiaabohaaeaacaqGubGaae4Baiaabs hacaqGHbGaaeiBaiaabccacaqGUbGaaeyDaiaab2gacaqGIbGaaeyz aiaabkhacaqGGaGaae4BaiaabAgacaqGGaGaaeyBaiaabggacaqGYb Gaae4Aaiaabohaaaaaaa@5419@

          = 85+76+90+85+39+48+56+95+81+75 10 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI4aGaaGynaiabgUcaRiaaiEdacaaI2aGaey4kaSIaaGyo aiaaicdacqGHRaWkcaaI4aGaaGynaiabgUcaRiaaiodacaaI5aGaey 4kaSIaaGinaiaaiIdacqGHRaWkcaaI1aGaaGOnaiabgUcaRiaaiMda caaI1aGaey4kaSIaaGioaiaaigdacqGHRaWkcaaI3aGaaGynaaqaai aaigdacaaIWaaaaaaa@4F53@

          = 730 10 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI3aGaaG4maiaaicdaaeaacaaIXaGaaGimaaaaaaa@3A9B@

          =73 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4naiaaiodaaaa@385C@

Thus, the mean marks obtained by the group of students is 73.

Question: 7

The enrolment in a school during six consecutive years was as follows:

1555, 1670, 1750, 2013, 2540, 2820

Find the mean enrolment of the school for this period.

Solution

Mean enrolment

= Sum of numbers of enrolment Total number of enrolment MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa aeOBaiaabwhacaqGTbGaaeOyaiaabwgacaqGYbGaae4Caiaabccaca qGVbGaaeOzaiaabccacaqGLbGaaeOBaiaabkhacaqGVbGaaeiBaiaa b2gacaqGLbGaaeOBaiaabshaaeaacaqGubGaae4BaiaabshacaqGHb GaaeiBaiaabccacaqGUbGaaeyDaiaab2gacaqGIbGaaeyzaiaabkha caqGGaGaae4BaiaabAgacaqGGaGaaeyzaiaab6gacaqGYbGaae4Bai aabYgacaqGTbGaaeyzaiaab6gacaqG0baaaaaa@654F@  

= 1555+1670+1750+2013+2540+2820 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaGaaGynaiaaiwdacaaI1aGaey4kaSIaaGymaiaaiAda caaI3aGaaGimaiabgUcaRiaaigdacaaI3aGaaGynaiaaicdacqGHRa WkcaaIYaGaaGimaiaaigdacaaIZaGaey4kaSIaaGOmaiaaiwdacaaI 0aGaaGimaiabgUcaRiaaikdacaaI4aGaaGOmaiaaicdaaeaacaaI2a aaaaaa@4DD0@  

= 12348 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaGaaGOmaiaaiodacaaI0aGaaGioaaqaaiaaiAdaaaaa aa@3B62@  

=2058 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG OmaiaaicdacaaI1aGaaGioaaaa@39D5@  

Thus, the mean enrolment of the school is 2,058 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiaacY cacaaIWaGaaGynaiaaiIdaaaa@397F@ .

Question: 8

The rainfall (in mm) in a city on 7 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4naaaa@3699@  days of a certain week was recorded as follows:

Day

Mon

Tue

Wed

Thurs

Fri

Sat

Sun

Rainfall (in mm)

0.0

12.2

2.1

0.0

20.5

5.5

1.0

 

(i)              Find the range of the rainfall in the above data.

(ii)           Find the mean rainfall for the week.

(iii)         On how many days was the rainfall less than the mean rainfall.

Solution

(i)              The range of the rainfall

=Highest rainfallLowest rainfall MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaae isaiaabMgacaqGNbGaaeiAaiaabwgacaqGZbGaaeiDaiaabccacaqG YbGaaeyyaiaabMgacaqGUbGaaeOzaiaabggacaqGSbGaaeiBaiabgk HiTiaabYeacaqGVbGaae4DaiaabwgacaqGZbGaaeiDaiaabccacaqG YbGaaeyyaiaabMgacaqGUbGaaeOzaiaabggacaqGSbGaaeiBaaaa@53C4@

          =20.50.0=20.5 mm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG OmaiaaicdacaGGUaGaaGynaiabgkHiTiaaicdacaGGUaGaaGimaiab g2da9iaaikdacaaIWaGaaiOlaiaaiwdacaqGGaGaaeyBaiaab2gaaa a@4348@

(ii)           Mean rainfall

= Sum of rainfall recorded Total number of days MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa aeOCaiaabggacaqGPbGaaeOBaiaabAgacaqGHbGaaeiBaiaabYgaca qGGaGaaeOCaiaabwgacaqGJbGaae4BaiaabkhacaqGKbGaaeyzaiaa bsgaaeaacaqGubGaae4BaiaabshacaqGHbGaaeiBaiaabccacaqGUb GaaeyDaiaab2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4BaiaabAga caqGGaGaaeizaiaabggacaqG5bGaae4Caaaaaaa@5DE0@

          = 0.0+12.2+2.1+2.2+20.5+5.5+1.0 7 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIWaGaaiOlaiaaicdacqGHRaWkcaaIXaGaaGOmaiaac6ca caaIYaGaey4kaSIaaGOmaiaac6cacaaIXaGaey4kaSIaaGOmaiaac6 cacaaIYaGaey4kaSIaaGOmaiaaicdacaGGUaGaaGynaiabgUcaRiaa iwdacaGGUaGaaGynaiabgUcaRiaaigdacaGGUaGaaGimaaqaaiaaiE daaaaaaa@4D97@

          = 41.3 7 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaI0aGaaGymaiaac6cacaaIZaaabaGaaG4naaaaaaa@3A97@

          =5.9mm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ynaiaac6cacaaI5aGaaGjbVlaab2gacaqGTbaaaa@3C7F@

(iii)         5 days. i.e., Monday, Wednesday, Thursday, Saturday and Sunday, rainfalls were less than the mean rainfall.

Question: 9

The heights of 10 girls were measured in cm and the results are as follows:

135, 150, 139, 128, 151, 132, 146, 149, 143, 141.

(i)              What is the height of the tallest girl?

(ii)           What is the height of the shortest girl?

(iii)         What is the range of the data?

(iv)         What is the mean height of the girls?

(v)            How many girls have heights more than the mean height.

Solution

(i)      The height of the tallest girl =151 cm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaiwdacaaIXaGaaeiiaiaabogacaqGTbaaaa@3B8C@  

(ii)    The height of the shortest girl =128 cm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaikdacaaI4aGaaiiOaiaaysW7caqGJbGaaeyBaaaa@3D9E@   

(iii)         The range of the data =Highest heightLowest height MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaae isaiaabMgacaqGNbGaaeiAaiaabwgacaqGZbGaaeiDaiaabccacaqG ObGaaeyzaiaabMgacaqGNbGaaeiAaiaabshacqGHsislcaqGmbGaae 4BaiaabEhacaqGLbGaae4CaiaabshacaqGGaGaaeiAaiaabwgacaqG PbGaae4zaiaabIgacaqG0baaaa@5018@

          =151128=23 cm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaiwdacaaIXaGaeyOeI0IaaGymaiaaikdacaaI4aGaeyypa0Ja aGOmaiaaiodacaqGGaGaae4yaiaab2gaaaa@4131@

(iv)         The mean height

          = Sum of heights of the girsl Total numebr of girls MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaqGtbGaaeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGa aeiAaiaabwgacaqGPbGaae4zaiaabIgacaqG0bGaae4Caiaabccaca qGVbGaaeOzaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaae4zaiaa bMgacaqGYbGaae4CaiaabYgaaeaacaqGubGaae4BaiaabshacaqGHb GaaeiBaiaabccacaqGUbGaaeyDaiaab2gacaqGLbGaaeOyaiaabkha caqGGaGaae4BaiaabAgacaqGGaGaae4zaiaabMgacaqGYbGaaeiBai aabohaaaaaaa@612E@

          = 135+150+139+128+151+132 +146+149+143+141 10 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaqaabeqaaiaaigdacaaIZaGaaGynaiabgUcaRiaaigdacaaI1aGa aGimaiabgUcaRiaaigdacaaIZaGaaGyoaiabgUcaRiaaigdacaaIYa GaaGioaiabgUcaRiaaigdacaaI1aGaaGymaiabgUcaRiaaigdacaaI ZaGaaGOmaaqaaiabgUcaRiaaigdacaaI0aGaaGOnaiabgUcaRiaaig dacaaI0aGaaGyoaiabgUcaRiaaigdacaaI0aGaaG4maiabgUcaRiaa igdacaaI0aGaaGymaaaabaGaaGymaiaaicdaaaaaaa@5683@

          =  1414 10 =141.4 cm MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacqGH9a qpcaGGGcWaaSaaaeaacaaIXaGaaGinaiaaigdacaaI0aaabaGaaGym aiaaicdaaaaabaGaeyypa0JaaGymaiaaisdacaaIXaGaaiOlaiaais dacaqGGaGaae4yaiaab2gaaaaa@43A3@

(v)            Five girls, i.e., 150, 151, 146, 149, 143 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiw dacaaIWaGaaiilaiaabccacaaIXaGaaGynaiaaigdacaGGSaGaaeii aiaaigdacaaI0aGaaGOnaiaacYcacaqGGaGaaGymaiaaisdacaaI5a GaaiilaiaabccacaaIXaGaaGinaiaaiodaaaa@4638@ , have heights (in cm) more than the mean height.

 

Exercise: 3.2 (5)

 

Question: 1

The scores in mathematics test (out of 25) of 15 students is as follows:

19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20

Find the mode and median of this data. Are they same?

Solution

Arranging the given data in ascending order,

5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaiaacY cacaqGGaGaaGyoaiaacYcacaqGGaGaaGymaiaaicdacaGGSaGaaeii aiaaigdacaaIYaGaaiilaiaabccacaaIXaGaaGynaiaacYcacaqGGa GaaGymaiaaiAdacaGGSaGaaeiiaiaaigdacaaI5aGaaiilaiaabcca caaIYaGaaGimaiaacYcacaqGGaGaaGOmaiaaicdacaGGSaGaaeiiai aaikdacaaIWaGaaiilaiaabccacaaIYaGaaGimaiaacYcacaqGGaGa aGOmaiaaiodacaGGSaGaaeiiaiaaikdacaaI0aGaaiilaiaabccaca aIYaGaaGynaiaacYcacaqGGaGaaGOmaiaaiwdaaaa@5D04@

Mode is the observation occurred the highest number of times. Therefore, Mode =20 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG Omaiaaicdaaaa@3854@

Median is the middle observation =20 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG Omaiaaicdaaaa@3854@

Yes, Mode and Median are same for given observation.

Question: 2

The runs scored in a cricket match by 11 players is as follows:

6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15

Find the mean, mode and median of this data. Are the three same?

Solution

Arranging the given data in ascending order,

6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOnaiaacY cacaqGGaGaaGioaiaacYcacaqGGaGaaGymaiaaicdacaGGSaGaaeii aiaaigdacaaIWaGaaiilaiaabccacaaIXaGaaGynaiaacYcacaqGGa GaaGymaiaaiwdacaGGSaGaaeiiaiaaigdacaaI1aGaaiilaiaabcca caaI1aGaaGimaiaacYcacaqGGaGaaGioaiaaicdacaGGSaGaaeiiai aaigdacaaIWaGaaGimaiaacYcacaqGGaGaaGymaiaaikdacaaIWaaa aa@5345@

Mean =  Sum of observations Number of observations MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeytaiaabw gacaqGHbGaaeOBaiaabccacqGH9aqpcaqGGaWaaSaaaeaacaqGtbGa aeyDaiaab2gacaqGGaGaae4BaiaabAgacaqGGaGaae4Baiaabkgaca qGZbGaaeyzaiaabkhacaqG2bGaaeyyaiaabshacaqGPbGaae4Baiaa b6gacaqGZbaabaGaaeOtaiaabwhacaqGTbGaaeOyaiaabwgacaqGYb Gaaeiiaiaab+gacaqGMbGaaeiiaiaab+gacaqGIbGaae4Caiaabwga caqGYbGaaeODaiaabggacaqG0bGaaeyAaiaab+gacaqGUbGaae4Caa aaaaa@60C2@

=  6+8+10+10+15+15+15+50+80+100+120 11 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaae iiamaalaaabaGaaGOnaiabgUcaRiaaiIdacqGHRaWkcaaIXaGaaGim aiabgUcaRiaaigdacaaIWaGaey4kaSIaaGymaiaaiwdacqGHRaWkca aIXaGaaGynaiabgUcaRiaaigdacaaI1aGaey4kaSIaaGynaiaaicda cqGHRaWkcaaI4aGaaGimaiabgUcaRiaaigdacaaIWaGaaGimaiabgU caRiaaigdacaaIYaGaaGimaaqaaiaaigdacaaIXaaaaaaa@520A@

=  429 11 =39 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0Jaae iiamaalaaabaGaaGinaiaaikdacaaI5aaabaGaaGymaiaaigdaaaGa eyypa0JaaG4maiaaiMdaaaa@3DCA@

Mode is the observation occurred the highest number of times =15 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaiwdaaaa@3858@

Median is the middle observation =15 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaiwdaaaa@3858@

Therefore, Mode and Median is 15 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiw daaaa@3752@ .

No, the mean, median and mode are not same.

Question: 3

The weights (in kg.) of 15 students of a class are:

38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47

(i)              Find the mode and median of this data.

(ii)           Is there more than one mode?

Solution

Arrange the given data in ascending order.

32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaG4maiaaik dacaGGSaGaaeiiaiaaiodacaaI1aGaaiilaiaabccacaaIZaGaaGOn aiaacYcacaqGGaGaaG4maiaaiEdacaGGSaGaaeiiaiaaiodacaaI4a GaaiilaiaabccacaaIZaGaaGioaiaacYcacaqGGaGaaG4maiaaiIda caGGSaGaaeiiaiaaisdacaaIWaGaaiilaiaabccacaaI0aGaaGOmai aacYcacaqGGaGaaGinaiaaiodacaGGSaGaaeiiaiaaisdacaaIZaGa aiilaiaabccacaaI0aGaaG4maiaacYcacaqGGaGaaGinaiaaiwdaca GGSaGaaeiiaiaaisdacaaI3aGaaiilaiaabccacaaI1aGaaGimaaaa @5EA7@

Mode is the observation occurred the highest number of times.

Therefore, Mode =38 and 43 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4maiaaiIdacaqGGaGaaeyyaiaab6gacaqGKbGaaeiiaiaaisdacaaI Zaaaaa@3DDA@

Median is the middle observation which is 40.

Yes, there are 2 modes

Question: 4

Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14

Solution

Arrange the given data in ascending order,

12, 12, 13, 13, 14, 14, 14, 16, 19 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaik dacaGGSaGaaeiiaiaaigdacaaIYaGaaiilaiaabccacaaIXaGaaG4m aiaacYcacaqGGaGaaGymaiaaiodacaGGSaGaaeiiaiaaigdacaaI0a GaaiilaiaabccacaaIXaGaaGinaiaacYcacaqGGaGaaGymaiaaisda caGGSaGaaeiiaiaaigdacaaI2aGaaiilaiaabccacaaIXaGaaGyoaa aa@4DB2@

Mode is the observation occurred the highest number of times. Thus, mode =14 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ymaiaaisdaaaa@3857@

Median is the middle observation which is 14.

Question: 5

Tell whether the statement is true or false:

(i)              The mode is always one of the numbers in a data.

(ii)           The mean can be one of the numbers in a data.

(iii)         The median is always one of the numbers in a data.

(iv)         The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

Solution

(i)              True

(ii)           False

(iii)         True

(iv)         False

 

Exercise: 3.3 (6)

 

Question: 1

Use the bar graph (Fig 3.3) to answer the following questions.

(a)           Which is the most popular pet?

 

 

 

Fig 3.3

 

 

 

(b)           How many children have dog as a pet?

Solution

a.   Cat is the most popular pet.

b.   8 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGioaaaa@369A@  students have dogs as a pet.

Question: 2

Read the bar graph (Fig 3.4) which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:

 

 

                   Fig 3.4

(i)              About how many books were sold in 1989? 1990? 1992?

(ii)           In which year were about 475 books sold? About 225 books sold?

(iii)         In which years were fewer than 250 books sold?

(iv)         Can you explain how you would estimate the number of books sold in 1989?

Solution

According to the given bar graph,

(i)              (a) In year 1989,180 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiM dacaaI4aGaaGyoaiaacYcacaaMe8UaaGymaiaaiIdacaaIWaaaaa@3D4F@  books were sold. (b) In year 1990,475 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiM dacaaI5aGaaGimaiaacYcacaaMe8UaaGinaiaaiEdacaaI1aaaaa@3D4E@  books were sold. (c) In year 1992,225 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiM dacaaI5aGaaGOmaiaacYcacaaMe8UaaGOmaiaaikdacaaI1aaaaa@3D49@  books were sold.

(ii)           In year 1990 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiM dacaaI5aGaaGimaaaa@38D3@ , about 475 books were sold and in year 1992 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiM dacaaI5aGaaGOmaaaa@38D5@ , about 225 books were sold.

(iii)         In years 1989 and 1992 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaaiM dacaaI4aGaaGyoaiaabccacaqGHbGaaeOBaiaabsgacaqGGaGaaGym aiaaiMdacaaI5aGaaGOmaaaa@3FDA@  fewer than 250 books were sold.

(iv)         By reading the graph, we calculate that 180 books were sold in year 1989.

Question: 3

Number of children in six different classes are given below. Represent the data on a bar graph.

Class

Fifth

Sixth

Seventh

Eighth

Ninth

Tenth

Number of Children

135

120

95

100

90

80

 

a.   How would you choose a scale.

b.   Answer the following questions:

(i)              Which class has the maximum number of children? And the minimum?

(ii)           Find the ratio of students of class sixth to the students of class eight.

Solution

Data represented by the bar graph is as follows:

 

 

 

 

a.   Scale:   1 unit=25 children MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaabc cacaqG1bGaaeOBaiaabMgacaqG0bGaeyypa0JaaGOmaiaaiwdacaqG GaGaae4yaiaabIgacaqGPbGaaeiBaiaabsgacaqGYbGaaeyzaiaab6 gaaaa@4587@

b.   (i) Fifth class has the maximum number of children and Tenth class has the minimum number of children.

(ii)        Ratio= Number of students in class sixth number of students in class eighth MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabg gacaqG0bGaaeyAaiaab+gacqGH9aqpdaWcaaqaaiaab6eacaqG1bGa aeyBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzaiaabccaca qGZbGaaeiDaiaabwhacaqGKbGaaeyzaiaab6gacaqG0bGaae4Caiaa bccacaqGPbGaaeOBaiaabccacaqGJbGaaeiBaiaabggacaqGZbGaae 4CaiaabccacaqGZbGaaeyAaiaabIhacaqG0bGaaeiAaaqaaiaab6ga caqG1bGaaeyBaiaabkgacaqGLbGaaeOCaiaabccacaqGVbGaaeOzai aabccacaqGZbGaaeiDaiaabwhacaqGKbGaaeyzaiaab6gacaqG0bGa ae4CaiaabccacaqGPbGaaeOBaiaabccacaqGJbGaaeiBaiaabggaca qGZbGaae4CaiaabccacaqGLbGaaeyAaiaabEgacaqGObGaaeiDaiaa bIgaaaaaaa@7718@

        = 120 100 = 6 5 =6:5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaGaaGOmaiaaicdaaeaacaaIXaGaaGimaiaaicdaaaGa eyypa0ZaaSaaaeaacaaI2aaabaGaaGynaaaacqGH9aqpcaaI2aGaai Ooaiaaiwdaaaa@4126@

Question: 4

The performance of students in 1st Term and 2nd Term is given. Draw a double bar graph choosing appropriate scale and answer the following:

Subject

English

Hindi

Maths

Science

S. Science

1st Term
(M.M. 100)

67

72

88

81

73

2nd Term
(M.M. 100)

70

65

95

85

75

 

(i)              In which subject, has the child improved his performance the most?

(ii)           In which subject is the improvement the least?

(iii)         Has the performance gone down in any subject?

Solution

Data represented by bar graph is as follows:

 

 

 

 

 

Difference of marks of 1st term and 2nd term

English =7067=3 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4naiaaicdacqGHsislcaaI2aGaaG4naiabg2da9iaaiodaaaa@3C8A@

Hindi                       =6572=7 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG OnaiaaiwdacqGHsislcaaI3aGaaGOmaiabg2da9iabgkHiTiaaiEda aaa@3D7B@

Maths                     =9588=7 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG yoaiaaiwdacqGHsislcaaI4aGaaGioaiabg2da9iaaiEdaaaa@3C98@

Science                   =8581=4 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG ioaiaaiwdacqGHsislcaaI4aGaaGymaiabg2da9iaaisdaaaa@3C8D@

S. Science               =7573=2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4naiaaiwdacqGHsislcaaI3aGaaG4maiabg2da9iaaikdaaaa@3C8B@

(i)              The child has improved most in Maths subject.

(ii)           In S. Science subject, the child improvement is least.

(iii)         Yes, in Hindi subject, the child performance has gone down.

Question: 5

Consider this data collected from a survey of a colony.

Favourite Sport

Cricket

Basket Ball

Swimming

Hockey

Athletics

Watching

1240

470

510

423

250

Participating

620

320

320

250

105

 

(i)              Draw a double bar graph choosing an appropriate scale.

          What do you infer from the bar graph?

(ii)           Which sport is most popular?

(iii)         Which is more preferred, watching or participating in sports?

Solution

Data represented by the double bar graph is as follows:

(i)              This bar graph represents the number of persons who are watching and participating in their favourite sports.

 

 

 

 

 

 

(ii)           Cricket is most popular.

(iii)         Watching sports is more preferred.

Question: 6

Take the data giving the minimum and the maximum temperature of various cities given in the beginning of this chapter (Table 3.1). Plot a double bar graph using the data and answer the following:

Table 3.1

Temperatures of cities as on 20.6.2006

 

Max.

Min.

Ahmedabad

38°C

29°C

Amritsar

37°C

26°C

Bangalore

28°C

21°C

Chennai

36°C

27°C

Delhi

38°C

28°C

Jaipur

39°C

29°C

Jammu

41°C

26°C

Mumbai

32°C

27°C

 

(i)              Which city has the largest difference in the minimum and maximum temperature on the given date?

(ii)           Which is the hottest city and which is the coldest city?

(iii)         Name two cities where maximum temperature of one was less than the minimum temperature of the other.

(iv)         Name the city which has the least difference between its minimum and the maximum temperature.

Solution

Data represented by double bar graph is as follows:

 

 

 

 

(i)              Jammu has the largest difference in temperature i.e.,

          Maximum temperature =41°Cand MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG inaiaaigdacqGHWcaScaqGdbGaaGjbVlaabggacaqGUbGaaeizaaaa @3F52@

          Minimum temperature =26°C. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG OmaiaaiAdacqGHWcaScaqGdbGaaeOlaaaa@3BBD@

           Difference=41°C26°C=15°C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyinIWLaae iiaiaabseacaqGPbGaaeOzaiaabAgacaqGLbGaaeOCaiaabwgacaqG UbGaae4yaiaabwgacqGH9aqpcaaI0aGaaGymaiabgclaWkaaboeacq GHsislcaaIYaGaaGOnaiabgclaWkaaboeacqGH9aqpcaaIXaGaaGyn aiabgclaWkaaboeaaaa@5040@

(ii)           Jammu is the hottest city due to maximum temperature is high and Bangalore is the coldest city due to maximum temperature is low.

(iii)         Maximum temperature of Bangalore is 28°C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiaaiI dacqGHWcaScaqGdbaaaa@3A08@

          Minimum temperature of two cities whose minimum temperature is higher than the maximum temperature of Bangalore are Ahmedabad and Jaipur where the minimum temperature is 29°C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaiaaiM dacqGHWcaScaqGdbaaaa@3A09@

(iv)         Mumbai has the least difference in temperature i.e.,

          Maximum temperature =32°Cand MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG 4maiaaikdacqGHWcaScaqGdbGaaGjbVlaabggacaqGUbGaaeizaaaa @3F52@

          Minimum temperature =27°C. MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG OmaiaaiEdacqGHWcaScaqGdbGaaeOlaaaa@3BBE@

           Difference=32°C27°C=5°C MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyinIWLaae iiaiaabseacaqGPbGaaeOzaiaabAgacaqGLbGaaeOCaiaabwgacaqG UbGaae4yaiaabwgacqGH9aqpcaaIZaGaaGOmaiabgclaWkaaboeacq GHsislcaaIYaGaaG4naiabgclaWkaaboeacqGH9aqpcaaI1aGaeyiS aaRaae4qaaaa@4F86@

 

Exercise: 3.4 (4)

 

Question: 1

Tell whether the following is certain to happen, impossible, can happen but not certain.

(i)              You are older today than yesterday.

(ii)           A tossed coin will land heads up.

(iii)         A die when tossed shall land up with 8 on top.

(iv)         The next traffic light seen will be green.

(v)            Tomorrow will be a cloudy day.

Solution

(i)              It is certain to happen.

(ii)           It can happen but not certain.

(iii)         It is impossible.

(iv)         It can happen but not certain.

(v)            It can happen but not certain.

Question: 2

There are 6 marbles in a box with numbers from 1 to 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaabc cacaqG0bGaae4BaiaabccacaaI2aaaaa@3A82@  marked on each of them.

(i)              What is the probability of drawing a marble with number 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaaaa@3694@ ?

(ii)           What is the probability of drawing a marble with number 5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaaaa@3697@ ?

Solution

Total marbles from 1 to 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaabc cacaqG0bGaae4BaiaabccacaaI2aaaaa@3A82@  marked in a box =6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0JaaG Onaaaa@379E@

(i)              The probability of drawing a marble with number 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGOmaaaa@3694@  

          =  P(drawing one marble)= 1 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeypaiaabc cacaqGGaGaaeiuaiaabIcacaqGKbGaaeOCaiaabggacaqG3bGaaeyA aiaab6gacaqGNbGaaeiiaiaab+gacaqGUbGaaeyzaiaabccacaqGTb GaaeyyaiaabkhacaqGIbGaaeiBaiaabwgacaqGPaGaeyypa0ZaaSaa aeaacaaIXaaabaGaaGOnaaaaaaa@4CB0@

(ii)           The probability of drawing a marble with number 5 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGynaaaa@3697@

          = P(drawing one marble)= 1 6 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeypaiaabc cacaqGqbGaaeikaiaabsgacaqGYbGaaeyyaiaabEhacaqGPbGaaeOB aiaabEgacaqGGaGaae4Baiaab6gacaqGLbGaaeiiaiaab2gacaqGHb GaaeOCaiaabkgacaqGSbGaaeyzaiaabMcacqGH9aqpdaWcaaqaaiaa igdaaeaacaaI2aaaaaaa@4C0D@

Question: 3

A coin is flipped to decide which team starts the game. What is the probability that your team will start?

Solution

A coin has two possible outcomes Head and Tail.

Probability of getting Head or Tail is equal.

      P(Starting game)= 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyinIWLaae iiaiaabccacaqGGaGaaeiiaiaabccacaqGGaGaaeiuaiaabIcacaqG tbGaaeiDaiaabggacaqGYbGaaeiDaiaabMgacaqGUbGaae4zaiaabc cacaqGNbGaaeyyaiaab2gacaqGLbGaaeykaiabg2da9maalaaabaGa aGymaaqaaiaaikdaaaaaaa@4B4C@

Question: 4

A box contains pairs of socks of two colours (black and white). I have picked out a white sock. I pick out one more with my eyes closed. What is the probability that it will make a pair?

Solution

It can be observed that while closing the eyes, one can draw either a black sock or a white sock. Therefore, there are two possible cases.

Probability= Number of Favourable outcome Number of possible outcomes MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeiuaiaabk hacaqGVbGaaeOyaiaabggacaqGIbGaaeyAaiaabYgacaqGPbGaaeiD aiaabMhacqGH9aqpdaWcaaqaaiaab6eacaqG1bGaaeyBaiaabkgaca qGLbGaaeOCaiaabccacaqGVbGaaeOzaiaabccacaqGgbGaaeyyaiaa bAhacaqGVbGaaeyDaiaabkhacaqGHbGaaeOyaiaabYgacaqGLbGaae iiaiaab+gacaqG1bGaaeiDaiaabogacaqGVbGaaeyBaiaabwgaaeaa caqGobGaaeyDaiaab2gacaqGIbGaaeyzaiaabkhacaqGGaGaae4Bai aabAgacaqGGaGaaeiCaiaab+gacaqGZbGaae4CaiaabMgacaqGIbGa aeiBaiaabwgacaqGGaGaae4BaiaabwhacaqG0bGaae4yaiaab+gaca qGTbGaaeyzaiaabohaaaaaaa@7244@

Probability (a pair of white socks will be formed) = 1 2 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipE0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS aaaeaacaaIXaaabaGaaGOmaaaaaaa@3865@