# Following is the distribution of I.Q of 100 students. Find the median I.Q. 55 - 64, 65 - 74, 75 - 84, 85 - 84, 95 - 114

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Following is the distribution of I.Q of 100 students. Find the median I.Q.

 I. Q: 55 - 64 65 - 74 75 - 84 85 - 84 95 - 104 105 - 114 115 - 124 125 - 134 135 - 144 No. of students: 1 2 9 22 33 22 8 2 1

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 Class interval (exclusive) Class interval (inclusive) Frequency Cumulative frequency 55 - 64 54.5 - 64.5 1 1 65 - 74 64.5 - 74.5 2 3 75 - 84 74.5 - 84.5 9 12 85 - 94 84.5 - 94.5 22 34 (F) 95 - 104 94.5 - 104.5 33 (f) 37 105 - 114 104.5 - 114.5 22 89 115 - 124 114.5 - 114.5 8 97 125 - 134 114.5 - 124.5 2 99 135 - 144 134.5 - 144.5 1 100 N = 100

We have,

N = 100

$\frac{N}{2}=\frac{100}{2}=50$

The cumulative frequency just greater than $\frac{N}{2}$ s 67 then the median class 94.5-104.5 such that,

l = 94.5, f = 33, F = 34, h = 104.5 – 94.5 = 10

Median = I + $\frac{\frac{N}{2}-F}{f}\times h$

$=94.5+\frac{50-34}{33}\times10$

$=94.5+\frac{16}{33}\times10$

$=94.5+4.85=99.35$