Calculate the median for the following distribution.

$\begin{matrix} M a r k s o b t a i n e d & N u m b e r o f s t u d e n t s B e l o w 10 & 6 B e l o w 20 & 15 B e l o w 30 & 29 B e l o w 40 & 41 B e l o w 50 & 60 B e l o w 60 & 70 \end{matrix}$ [4 MARKS]

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Solution

Concept: 1 Mark
Application: 3 Marks

The frequency distribution table from the given distribution is as follows:

$\begin{matrix} C l a s s & N u m b e r o f & C u m u l a t i v e (M a r k s o b t a i n e d) & s t u d e n t s & f r e q u e n c y (f r e q u e n c y) 0 - 10 & 6 & 6 10 - 20 & 9 & 15 20 - 30 & 14 & 29 30 - 40 & 12 & 41 40 - 50 & 19 & 60 50 - 60 & 10 & 70 \end{matrix}$

n = 70 $∴ \frac{n}{2} = 35$ . This observation lies in the class 30 - 40. So, 30 - 40 is the median class.

$∴$ l = 30, h = 10, cf = 29, f = 12

Using the formula, Median $= l + (\frac{\frac{n}{2} - c f}{f}) \times h$ , we get

Median $= 30 + (\frac{35 - 29}{12}) \times 10 = 30 + 5 = 35$

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