Find the median for the following frequency distribution:

Class Interval
25-35
35-45
45-55
55-65
65-75
Frequency
20
25
5
7
4
Give answer upto the nearest integer value.

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Solution

$F o r c o n t i n u o u s d a t a, m e d i a n = L + (\frac{\frac{N}{2} - C}{f}) \times H W h e r e N = T o t a l c u m u l a t i v e f r e q u e n c y L = l o w e r l i m i t o f t h e m e d i a n c l a s s I n t e r v a l$
$; M e d i a n C l a s s = t h e c l a s s i n t e r v a l h a v i n g c u m u l a t i v e f r e q \geq \frac{N}{2} l i e s C = C u m u l a t i v e f r e q u e n c y o f t h e c l a s s i n t e r v a l j u s t b e f o r e t h e m e d i a n c l a s s i n t e r v a l f = f r e q u e n c y o f t h e m e d i a n c l a s s i n t e r v a l; H = w i d t h o f t h e m e d i a n c l a s s$
$i n t e r v a l / / H e r e N = 61 \frac{N}{2} = 30.5, t h i s c u m u l a t i v e f r e q l i e s w i t h i n i n t e r v a l (35 - 45); L = 35 C = 20; f = 25; H = 10 H e n c e m e d i a n = 35 + (\frac{\frac{61}{2} - 20}{25} \times 10) = 35 + (\frac{30.5 - 20}{25} \times 10)$
$= 35 + (\frac{10.5}{25} \times 10) = 35 + \frac{105}{25} = 35 + 4.2 = 39.2$

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