A survey regarding the height (in cm) of 51 girls of class X of a school was conducted and the following data was obtained:

Height in cm	Number of Girls
Less than 140	4
Less than 145	11
Less than 150	29
Less than 155	40
Less than 160	46
Less than 165	51

Find the median height.

Given:

A survey regarding the height (in cm) of 51 girls of class X of a school was conducted.

To do:

We have to find the median height.

Solution:

Arranging the data in class intervals, we get,

Here,

$N=51$

This implies,

$\frac{N}{2}=\frac{51}{2}=25.5$

The cumulative frequency just greater than 25.5 is 29 and the corresponding class is 145 – 150. 

This implies, 145 – 150 is the median class.

Therefore,

$l = 145, f= 18, F =11$ and $h = 150-145=5$

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

Therefore,

Median $=145+\frac{25.5-11}{18}\times 5$

$=145+\frac{14.5}{18}\times 5$

$=145+\frac{72.5}{18}$

$=145+4.03$

$=149.03$

The median height is 149.03 cm.

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Updated on: 10-Oct-2022

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