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
|
|
2.
|
Aditi
|
|
3.
|
Nikhil
|
|
4.
|
Akhil
|
|
5.
|
Riya
|
|
6.
|
Akshat
|
|
7.
|
Abhishek
|
|
8.
|
Mayank
|
|
9.
|
Rahul
|
|
10.
|
Ayush
|
|
|
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 .
(ii)
The lowest number is .
(iii)
The range of the data is
(iv)
Arithmetic mean
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
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
Mean of score
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 or by ? 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
(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.
(iv)
To find the best performer, we should know the mean of all
the players played.
Mean score of player
Mean score of
player
Mean score of
player C
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
Lowest marks obtained by the student
(ii)
Range of marks
Highest marks Lowest marks
(iii)
Mean of obtained marks
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
Thus, the mean enrolment of the school is .
Question: 8
The
rainfall (in mm) in a city on 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
(ii)
Mean rainfall
(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
(ii) The height of
the shortest girl
(iii)
The range of the data
(iv)
The mean height
(v)
Five girls, i.e., ,
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,
Mode is the
observation occurred the highest number of times. Therefore, Mode
Median is the
middle observation
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,
Mode is the
observation occurred the highest number of times
Median is the
middle observation
Therefore, Mode
and Median is .
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.
Mode is the
observation occurred the highest number of times.
Therefore, Mode
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,
Mode is the
observation occurred the highest number of times. Thus, mode
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. 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 books were sold. (b) In year books were sold. (c) In year books were sold.
(ii)
In year ,
about 475 books were sold and in year ,
about 225 books were sold.
(iii)
In years 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:
b. (i) Fifth class has
the maximum number of children and Tenth class has the minimum number of
children.
(ii)
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
Hindi
Maths
Science
S. Science
(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
Minimum temperature
(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
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
(iv)
Mumbai has the least difference in
temperature i.e.,
Maximum temperature
Minimum temperature
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 marked on each of them.
(i)
What is the probability of drawing a marble with
number ?
(ii)
What is the probability of drawing a marble with
number ?
Solution
Total marbles
from marked in a box
(i)
The probability of drawing a marble with number
(ii)
The probability of drawing a marble with number
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.
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 (a
pair of white socks will be formed)