The following is the distribution of height of students of a certain class in a certain city:

Height (in cms):	160-162	163-165	166-168	169-171	172-174
No. of students:	15	118	142	127	18

Find the average height of maximum number of students.

Given:

The distribution of height of students of a certain class in a certain city.

To do:

We have to find the average height of maximum number of students.

Solution:

The frequency of the given data is as given below.

We observe that the class interval of 166-168 has the maximum frequency(142).

Therefore, it is the modal class.

Here,

$l=166, h=2, f=142, f_1=118, f_2=127$

We know that,

Mode $=l+\frac{f-f_1}{2 f-f_1-f_2} \times h$

$=166+\frac{142-118}{2 \times 142-118-127} \times 2$

$=166+\frac{24}{284-245} \times 2$

$=166+\frac{48}{39}$

$=166+1.3$

$=167.3$

Hence, the average height of maximum number of students is 167.3 cm.

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Updated on: 10-Oct-2022

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