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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 + \(\frac{\frac{N}{2}-F}{f}\times h\)

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

\(=94.5+\frac{16}{33}\times10\)

\(=94.5+4.85=99.35\)

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