Graphical Representation of Statistical Data - Exercise 23.3

# Graphical Representation of Statistical Data - Exercise 23.3 - Extra Documents & Tests for Class 9

``` Page 1

Q u e s t i o n : 3 7
Construct a histogram for the following data:

Monthly
School
fee (in Rs):
30-60 60-90 90-120 120-150 150-180 180-210 210-240
No of Schools 5 12 14 18 10 9 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 rupees.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 30-60 is big divisions.
2. The height of the rectangle corresponding to the class-interval 60-90 is big divisions.
3. The height of the rectangle corresponding to the class-interval 90-120 is big divisions.
4. The height of the rectangle corresponding to the class-interval 120-150 is big divisions.
Page 2

Q u e s t i o n : 3 7
Construct a histogram for the following data:

Monthly
School
fee (in Rs):
30-60 60-90 90-120 120-150 150-180 180-210 210-240
No of Schools 5 12 14 18 10 9 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 rupees.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 30-60 is big divisions.
2. The height of the rectangle corresponding to the class-interval 60-90 is big divisions.
3. The height of the rectangle corresponding to the class-interval 90-120 is big divisions.
4. The height of the rectangle corresponding to the class-interval 120-150 is big divisions.
5. The height of the rectangle corresponding to the class-interval 150-180 is big divisions.
6. The height of the rectangle corresponding to the class-interval 180-210 is big divisions.
7. The height of the rectangle corresponding to the class-interval 210-240 is big divisions.
The histogram of the given data is the following:
Q u e s t i o n : 3 8
The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on
the same axes.

Height (in cm):
124
to
128
128
to
132
132
to
136
136
to
140
140
to
144
144
to
148
148
to
152
152
to
156
156
to
160
160
to
164
No. of Children: 5 8 17 24 16 12 6 4 3 1
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights.
To draw the frequency polygon of the given data using histogram, obtain the mid-points of the upper horizontal side
of each rectangle and then join these mid-points of the adjacent rectangles of the histogram by line segments.
Obtain the mid-points of two class-intervals of 0 frequencies, i.e. on the horizontal axis, one adjacent to the first, on
its left and one adjacent to the last, on its right. These class-intervals are known as imagined class-intervals.
Complete the polygon by joining the mid-points of first and last class-intervals to the mid-points of imagined class-
intervals adjacent to them. Let us take one vertical division is equal to 4.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 124-128 is big
divisions.
2. The height of the rectangle corresponding to the class-interval 128-132 is big divisions.
3. The height of the rectangle corresponding to the class-interval 132-136 is  big
divisions.
Page 3

Q u e s t i o n : 3 7
Construct a histogram for the following data:

Monthly
School
fee (in Rs):
30-60 60-90 90-120 120-150 150-180 180-210 210-240
No of Schools 5 12 14 18 10 9 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 rupees.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 30-60 is big divisions.
2. The height of the rectangle corresponding to the class-interval 60-90 is big divisions.
3. The height of the rectangle corresponding to the class-interval 90-120 is big divisions.
4. The height of the rectangle corresponding to the class-interval 120-150 is big divisions.
5. The height of the rectangle corresponding to the class-interval 150-180 is big divisions.
6. The height of the rectangle corresponding to the class-interval 180-210 is big divisions.
7. The height of the rectangle corresponding to the class-interval 210-240 is big divisions.
The histogram of the given data is the following:
Q u e s t i o n : 3 8
The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on
the same axes.

Height (in cm):
124
to
128
128
to
132
132
to
136
136
to
140
140
to
144
144
to
148
148
to
152
152
to
156
156
to
160
160
to
164
No. of Children: 5 8 17 24 16 12 6 4 3 1
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights.
To draw the frequency polygon of the given data using histogram, obtain the mid-points of the upper horizontal side
of each rectangle and then join these mid-points of the adjacent rectangles of the histogram by line segments.
Obtain the mid-points of two class-intervals of 0 frequencies, i.e. on the horizontal axis, one adjacent to the first, on
its left and one adjacent to the last, on its right. These class-intervals are known as imagined class-intervals.
Complete the polygon by joining the mid-points of first and last class-intervals to the mid-points of imagined class-
intervals adjacent to them. Let us take one vertical division is equal to 4.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 124-128 is big
divisions.
2. The height of the rectangle corresponding to the class-interval 128-132 is big divisions.
3. The height of the rectangle corresponding to the class-interval 132-136 is  big
divisions.
4. The height of the rectangle corresponding to the class-interval 136-140 is  big divisions.
5. The height of the rectangle corresponding to the class-interval 140-144 is big divisions.
6. The height of the rectangle corresponding to the class-interval 144-148 is big divisions.
7. The height of the rectangle corresponding to the class-interval 148-152 is  big divisions.
8. The height of the rectangle corresponding to the class-interval 152-156 is  big divisions.
9. The height of the rectangle corresponding to the class-interval 156-160 is big
divisions.
10. The height of the rectangle corresponding to the class-interval 160-164 is big
divisions.
The histogram and frequency polygon of the given data is the following:

Q u e s t i o n : 3 9
The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
(a) Construct a frequency distribution for these data, using a class interval of 10 seconds.
(b) Draw a histogram to represent the frequency distribution.
S o l u t i o n :
Given that the times (in seconds) taken to solve a problem by each of 25 pupils are 16, 20, 26, 27, 28, 30, 33, 37,
38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52 and 20. The minimum and maximum time values are 16
and 64 respectively.
(a) At first construct the following frequency distribution for the given data. Since, the lowest value is 16; we start
with the class-interval 15-25, as the class size must be 10.
(b) To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
Page 4

Q u e s t i o n : 3 7
Construct a histogram for the following data:

Monthly
School
fee (in Rs):
30-60 60-90 90-120 120-150 150-180 180-210 210-240
No of Schools 5 12 14 18 10 9 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 rupees.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 30-60 is big divisions.
2. The height of the rectangle corresponding to the class-interval 60-90 is big divisions.
3. The height of the rectangle corresponding to the class-interval 90-120 is big divisions.
4. The height of the rectangle corresponding to the class-interval 120-150 is big divisions.
5. The height of the rectangle corresponding to the class-interval 150-180 is big divisions.
6. The height of the rectangle corresponding to the class-interval 180-210 is big divisions.
7. The height of the rectangle corresponding to the class-interval 210-240 is big divisions.
The histogram of the given data is the following:
Q u e s t i o n : 3 8
The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on
the same axes.

Height (in cm):
124
to
128
128
to
132
132
to
136
136
to
140
140
to
144
144
to
148
148
to
152
152
to
156
156
to
160
160
to
164
No. of Children: 5 8 17 24 16 12 6 4 3 1
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights.
To draw the frequency polygon of the given data using histogram, obtain the mid-points of the upper horizontal side
of each rectangle and then join these mid-points of the adjacent rectangles of the histogram by line segments.
Obtain the mid-points of two class-intervals of 0 frequencies, i.e. on the horizontal axis, one adjacent to the first, on
its left and one adjacent to the last, on its right. These class-intervals are known as imagined class-intervals.
Complete the polygon by joining the mid-points of first and last class-intervals to the mid-points of imagined class-
intervals adjacent to them. Let us take one vertical division is equal to 4.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 124-128 is big
divisions.
2. The height of the rectangle corresponding to the class-interval 128-132 is big divisions.
3. The height of the rectangle corresponding to the class-interval 132-136 is  big
divisions.
4. The height of the rectangle corresponding to the class-interval 136-140 is  big divisions.
5. The height of the rectangle corresponding to the class-interval 140-144 is big divisions.
6. The height of the rectangle corresponding to the class-interval 144-148 is big divisions.
7. The height of the rectangle corresponding to the class-interval 148-152 is  big divisions.
8. The height of the rectangle corresponding to the class-interval 152-156 is  big divisions.
9. The height of the rectangle corresponding to the class-interval 156-160 is big
divisions.
10. The height of the rectangle corresponding to the class-interval 160-164 is big
divisions.
The histogram and frequency polygon of the given data is the following:

Q u e s t i o n : 3 9
The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
(a) Construct a frequency distribution for these data, using a class interval of 10 seconds.
(b) Draw a histogram to represent the frequency distribution.
S o l u t i o n :
Given that the times (in seconds) taken to solve a problem by each of 25 pupils are 16, 20, 26, 27, 28, 30, 33, 37,
38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52 and 20. The minimum and maximum time values are 16
and 64 respectively.
(a) At first construct the following frequency distribution for the given data. Since, the lowest value is 16; we start
with the class-interval 15-25, as the class size must be 10.
(b) To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The above data is a continuous grouped frequency distribution with equal class-intervals, which is 10. Construct
rectangles with class-intervals as bases and respective frequencies as heights.
The histogram of the data in part (a) is as follows:

Q u e s t i o n : 4 0
Draw, in the same diagram, a histogram and a frequency polygon to represent the following data which shows the
monthly cost of living index of a city in a period of 2 years:

Cost of living
index:
440-
460
460-
480
480-500 500-520 520-540 540-560 560-580 580-600
No. of months: 2 4 3 5 3 2 1 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. To draw the frequency polygon of the given data using
histogram, obtain the mid-points of the upper horizontal side of each rectangle and then join these mid-points of the
adjacent rectangles of the histogram by line segments. Obtain the mid-points of two class-intervals of 0
frequencies, i.e. on the horizontal axis, one adjacent to the first, on its left and one adjacent to the last, on its right.
These class-intervals are known as imagined class-intervals. Complete the polygon by joining the mid-points of
first and last class-intervals to the mid-points of imagined class-intervals adjacent to them. Let us take one vertical
division is equal to 1 month.
The heights of the different rectangles are as follows:
1. The height of the rectangle corresponding to the class-interval 440-460 is 2 big divisions.
2. The height of the rectangle corresponding to the class-interval 460-480 is 4 big divisions.
3. The height of the rectangle corresponding to the class-interval 480-500 is 3 big divisions.
4. The height of the rectangle corresponding to the class-interval 500-520 is 5 big divisions.
5. The height of the rectangle corresponding to the class-interval 520-540 is 3 big divisions.
6. The height of the rectangle corresponding to the class-interval 540-560 is 2 big divisions.
7. The height of the rectangle corresponding to the class-interval 560-580is 1 big division.
Page 5

Q u e s t i o n : 3 7
Construct a histogram for the following data:

Monthly
School
fee (in Rs):
30-60 60-90 90-120 120-150 150-180 180-210 210-240
No of Schools 5 12 14 18 10 9 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. Let us take one vertical division is equal to 3 rupees.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 30-60 is big divisions.
2. The height of the rectangle corresponding to the class-interval 60-90 is big divisions.
3. The height of the rectangle corresponding to the class-interval 90-120 is big divisions.
4. The height of the rectangle corresponding to the class-interval 120-150 is big divisions.
5. The height of the rectangle corresponding to the class-interval 150-180 is big divisions.
6. The height of the rectangle corresponding to the class-interval 180-210 is big divisions.
7. The height of the rectangle corresponding to the class-interval 210-240 is big divisions.
The histogram of the given data is the following:
Q u e s t i o n : 3 8
The distribution of heights (in cm) of 96 children is given below. Construct a histogram and a frequency polygon on
the same axes.

Height (in cm):
124
to
128
128
to
132
132
to
136
136
to
140
140
to
144
144
to
148
148
to
152
152
to
156
156
to
160
160
to
164
No. of Children: 5 8 17 24 16 12 6 4 3 1
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights.
To draw the frequency polygon of the given data using histogram, obtain the mid-points of the upper horizontal side
of each rectangle and then join these mid-points of the adjacent rectangles of the histogram by line segments.
Obtain the mid-points of two class-intervals of 0 frequencies, i.e. on the horizontal axis, one adjacent to the first, on
its left and one adjacent to the last, on its right. These class-intervals are known as imagined class-intervals.
Complete the polygon by joining the mid-points of first and last class-intervals to the mid-points of imagined class-
intervals adjacent to them. Let us take one vertical division is equal to 4.
The heights of the different rectangles are as following
1. The height of the rectangle corresponding to the class-interval 124-128 is big
divisions.
2. The height of the rectangle corresponding to the class-interval 128-132 is big divisions.
3. The height of the rectangle corresponding to the class-interval 132-136 is  big
divisions.
4. The height of the rectangle corresponding to the class-interval 136-140 is  big divisions.
5. The height of the rectangle corresponding to the class-interval 140-144 is big divisions.
6. The height of the rectangle corresponding to the class-interval 144-148 is big divisions.
7. The height of the rectangle corresponding to the class-interval 148-152 is  big divisions.
8. The height of the rectangle corresponding to the class-interval 152-156 is  big divisions.
9. The height of the rectangle corresponding to the class-interval 156-160 is big
divisions.
10. The height of the rectangle corresponding to the class-interval 160-164 is big
divisions.
The histogram and frequency polygon of the given data is the following:

Q u e s t i o n : 3 9
The time taken, in seconds, to solve a problem by each of 25 pupils is as follows:
16, 20, 26, 27, 28, 30, 33, 37, 38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52, 20
(a) Construct a frequency distribution for these data, using a class interval of 10 seconds.
(b) Draw a histogram to represent the frequency distribution.
S o l u t i o n :
Given that the times (in seconds) taken to solve a problem by each of 25 pupils are 16, 20, 26, 27, 28, 30, 33, 37,
38, 40, 42, 43, 46, 46, 46, 48, 49, 50, 53, 58, 59, 60, 64, 52 and 20. The minimum and maximum time values are 16
and 64 respectively.
(a) At first construct the following frequency distribution for the given data. Since, the lowest value is 16; we start
with the class-interval 15-25, as the class size must be 10.
(b) To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The above data is a continuous grouped frequency distribution with equal class-intervals, which is 10. Construct
rectangles with class-intervals as bases and respective frequencies as heights.
The histogram of the data in part (a) is as follows:

Q u e s t i o n : 4 0
Draw, in the same diagram, a histogram and a frequency polygon to represent the following data which shows the
monthly cost of living index of a city in a period of 2 years:

Cost of living
index:
440-
460
460-
480
480-500 500-520 520-540 540-560 560-580 580-600
No. of months: 2 4 3 5 3 2 1 4
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. To draw the frequency polygon of the given data using
histogram, obtain the mid-points of the upper horizontal side of each rectangle and then join these mid-points of the
adjacent rectangles of the histogram by line segments. Obtain the mid-points of two class-intervals of 0
frequencies, i.e. on the horizontal axis, one adjacent to the first, on its left and one adjacent to the last, on its right.
These class-intervals are known as imagined class-intervals. Complete the polygon by joining the mid-points of
first and last class-intervals to the mid-points of imagined class-intervals adjacent to them. Let us take one vertical
division is equal to 1 month.
The heights of the different rectangles are as follows:
1. The height of the rectangle corresponding to the class-interval 440-460 is 2 big divisions.
2. The height of the rectangle corresponding to the class-interval 460-480 is 4 big divisions.
3. The height of the rectangle corresponding to the class-interval 480-500 is 3 big divisions.
4. The height of the rectangle corresponding to the class-interval 500-520 is 5 big divisions.
5. The height of the rectangle corresponding to the class-interval 520-540 is 3 big divisions.
6. The height of the rectangle corresponding to the class-interval 540-560 is 2 big divisions.
7. The height of the rectangle corresponding to the class-interval 560-580is 1 big division.
8. The height of the rectangle corresponding to the class-interval 580-600 is 4 big divisions.
The histogram and frequency polygon of the given data is as follows:

Q u e s t i o n : 4 1
The following is the distribution of total household expenditure (in Rs.) of manual worker in a city:

Expenditure
(in Rs):
100-
150
150-
200
200-
250
250-
300
300-
350
350-
400
400-
450
450-
500
No. of manual
workers:
25 40 33 28 30 22 16 8
Draw a histogram and a frequency polygon representing the above data.
S o l u t i o n :
To represent the given data by a histogram, we first draw horizontal and vertical axes. Let us consider that the
horizontal and vertical axes represent the class-limits and the frequencies of the class-intervals respectively.
The given data is a continuous grouped frequency distribution with equal class-intervals. Construct rectangles with
class-intervals as bases and respective frequencies as heights. It should be noted that the scale for horizontal
axis may not be same as the scale for vertical axis. To draw the frequency polygon of the given data using
histogram, obtain the mid-points of the upper horizontal side of each rectangle and then join these mid-points of the
adjacent rectangles of the histogram by line segments. Obtain the mid-points of two class-intervals of 0
frequencies, i.e. on the horizontal axis, one adjacent to the first, on its left and one adjacent to the last, on its right.
These class-intervals are known as imagined class-intervals. Complete the polygon by joining the mid-points of
first and last class-intervals to the mid-points of imagined class-intervals adjacent to them. Let us take one vertical
division is equal to 5 workers.
The heights of the different rectangles are as follows:
1. The height of the rectangle corresponding to the class-interval 100-150 is big divisions.
2. The height of the rectangle corresponding to the class-interval 150-200 is big divisions.
3. The height of the rectangle corresponding to the class-interval 200-250 is big
divisions.
4. The height of the rectangle corresponding to the class-interval 250-300 is big
divisions.
```

## Extra Documents & Tests for Class 9

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## Extra Documents & Tests for Class 9

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