The.following table gives the distribution of IQ of 100 students. Find the median IQ.
IQ
Frequency
75-84
8
85-94
11
95-104
26
105-114
31
115-124
18
125-134
4
135-144
2

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Solution

$F o r c o n t i n u o u s d a t a, m e d i a n = L + (\frac{\frac{N}{2} - C}{f}) \times H W h e r e N = T o t a l c u m u l a t i v e f r e q u e n c y L = l o w e r l i m i t o f t h e m e d i a n c l a s s I n t e r v a l; M e d i a n C l a s s = t h e c l a s s i n t e r v a l$
$h a v i n g c u m u l a t i v e f r e q \geq \frac{N}{2} l i e s C = c u m u l a t i v e f r e q u e n c y o f t h e c l a s s i n t e r v a l j u s t b e f o r e t h e m e d i a n c l a s s i n t e r v a l f = f r e q u e n c y o f t h e m e d i a n c l a s s i n t e r v a l; H = w i d t h o f t h e m e d i a n c l a s s$
$i n t e r v a l$
$H e r e N = 100 \frac{N}{2} = 50, t h i s c u m u l a t i v e f r e q l i e s w i t h i n i n t e r v a l (35 - 40); L = 105; C = 45; f = 31; H = 5 H e n c e m e d i a n = 105 + (\frac{\frac{100}{2} - 45}{31} \times 10) = 105 + (\frac{50 - 45}{31} \times 10) = 105 + (\frac{5}{31} \times 10) = 105 + \frac{50}{31}$
$= 105 + 1.61 = 106.6$

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