Find the median of following data.

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Solution

$M a r k s$ $N o . o f s t u d e n t s$
$f_{i}$ $c f$
$20 - 30$ $5$ $5$
$30 - 40$ $15$ $20$
$40 - 50$ $25$ $45$
$50 - 60$ $20$ $65$
$60 - 70$ $7$ $72$
$70 - 80$ $8$ $80$
$80 - 90$ $10$ $90$
$\sum f_{i} = 90$
$\Rightarrow$ $N = 90$ then, $\frac{N}{2} = \frac{90}{2} = 45$
$∴$ Median class $= 40 - 50$
$l = 40, f = 25, c f = 20$ and $h = 10$
$M e d i a n = l + \frac{\frac{N}{2} - c f}{f} \times h$

$= 40 + \frac{45 - 20}{25} \times 10$

$= 40 + 10$
$= 50$

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