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

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

Find the median height.

Given:

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

To do:

We have to find the median height.

Solution:

Arranging the classes in exclusive form and then forming its cumulative frequency table as below, we get,

Here,

$N = 420$

$\frac{N}{2} = \frac{420}{2} = 210$

The cumulative frequency just greater than $\frac{N}{2}$ is 275 and the corresponding class is 165.5 – 168.5. 

This implies, 165.5 – 168.5 is the median class.

Therefore,

$l = 165.5, f = 142, F = 133$ and $h = (168.5 - 165.5) = 3$

Medain $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$

$=165.5+\frac{210-133}{142} \times 3$

$=165.5+\frac{77}{142} \times 3$

$=165.5+\frac{231}{142}$

$= 165.5 + 1.63$

$= 167.13$

The median height is 167.13 cms.

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Updated on: 10-Oct-2022

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