ML Aggarwal Solution Class 10 Chapter 21 Measures of Central Tendency Exercise 21.4

 Exercise 21.4

Question 1

Draw a histogram for the following frequency distribution and find the mode from the graph :

Class 0-5 5-10 10-15 15-20 20-25 25-30
Frequency 2 5 18 14 8 5

Sol :














Mode=14


Question 2

Find the modal height of the following distribution by drawing a histogram :

Height(in cm) 140-150 150-160 160-170 170-180 180-190
No. of students 7 6 4 10 2

Sol :

Height (in cm)No. of students
140-1507
150-1606
160-1704
170-18010
180-1902









Now present the Height on x-axis and No. of students (frequency) on the y-axis

and draw a histogram as shown. In the histogram join AB and CD intersecting at M.
From M, draw MN to the x-axis. N shows the mode.
Hence mode = 174 cm


Question 3

A Mathematics aptitude test of 50 students was recorded as follows :

Marks 50-60 60-70 70-80 80-90 90-100
No. of students 4 8 14 19 5
Draw a histogram for the above data using a graph paper and locate the mode. (2011)

Sol :










Hence, the required mode is 82.5.


Question 4

Draw a histogram and estimate the mode for the following frequency distribution :

Class 0-10 10-20 20-30 30-40 40-50 50-60
Frequency 2 8 10 5 4 3

Sol :

Classes Frequency
0-10 2
10-20 8
20-30 10
30-40 5
40-50 4
50-60 3









Representing classes on x-axis and frequency on the y-axis,

we draw a histogram as shown.

In the histogram, join AB and CD intersecting at M.

From M, draw ML perpendicular to the x-axis. L shows the mode

Hence Mode = 23


Question 5

IQ of 50 students was recorded as follows

IQ score 80-00 90-100 100-110 110-120 120-130 130-140
No. of students 6 9 16 13 4 2
Draw a histogram for the above data and estimate the mode.

Sol :

IQ score No. of students
80-90 6
90-100 9
100-110 16
110-120 13
120-130 4
130-140 2








Representing the IQ scores on x-axis and number of students on the y-axis,

We draw a histogram as shown. Join AB and CD intersecting each other at M.
From M draw ML ⊥ x-axis. L is the mode which is 107

Question 6

Use a graph paper for this question. The daily pocket expenses of 200 students in a school are given below:

Pocket expenses
(in Rs)		 No. of students
(frequency)
0-5 10
5-10 14
10-15 28
15-20 42
20-25 50
25-30 30
30-35 14
35-40 12

Draw a histogram representing the above distribution and estimate the mode from the graph.


















Sol :
Mark the upper comers of the highest rectangle
and the corners of the adjacent rectangles as A, B, C, D as shown.
Join AC and BD to intersect at P. Draw PM ⊥ x-axis.
Then the abscissa of M is 21, which is the required mode.
Hence, mode = 21

Question 7

Draw a histogram for the following distribution :

Weight in kg 40-44 45-49 50-54 55-59 60-64 65-69
No. of students 2 8 12 10 6 4

Hence estimate the modal weight.
Sol :
We write the given distribution in the continuous form :
Weight in kg No. of students
39.5-44.5 2
44.5-49.5 8
49.5-54.5 12
54.5-59.5 10
59.5-64.5 6
64.5-69.5 4








Representing the weight (in kg) on x-axis

and No. of students on y-axis. We draw a histogram as shown.
Now join AB and CD intersecting each other at M.
From M, draw ML perpendicular to x-axis.
L is the mode which is 51.5 kg

Question 8

Find the mode of the following distribution by drawing a histogram

Mid value 12 18 24 30 36 42 48
Frequency 20 12 8 24 16 8 12
Also state the modal class.
Sol :
Mid value ClassFrequency
129-1520
1815-2112
2421-278
3027-3324
3633-3916
4239-458
4845-5112
















Representing class on x-axis and frequency on the y-axis,
we draw a histogram as shown.
Join AB and CD intersecting each other at M.
From M, draw ML perpendicular to the x-axis.
L shows the mode which is 30.5 and class is 27-33.

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