Find the mode of the data given below:

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Solution

$C l a s s$ $F r e q u e n c y$
$19.5 - 29.5$ $15$
$29.5 - 39.5$ $20$
$39.5 - 49.5$ $50$
$49.5 - 59.5$ $30$
$59.5 - 69.5$ $10$
Here, maximum frequency is $50$
$∴$ Modal class $= 39.5 - 49.5$
$l = 39.5, f_{0} = 20, f_{1} = 50, f_{2} = 30, h = 10$
$M o d e = l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$

$= 39.5 + \frac{50 - 20}{(2 \times 50) - 20 - 30} \times 10$

$= 39.5 + 6$
$= 45.5$

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