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

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8

 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
140-150	7
150-160	6
160-170	4
170-180	10
180-190	2

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	Class	Frequency
12	9-15	20
18	15-21	12
24	21-27	8
30	27-33	24
36	33-39	16
42	39-45	8
48	45-51	12

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.