Question

The median of 100 observations grouped in classes of equal width is 25. If the median class interval is 20 - 30 and the number of observations less than 20 is 45, then the frequency of median class is

• A. 10
• B. 20
• C. 15
• D. 12

Answer 1

Answer: (A)

Median is given as $M = l + \frac{\frac{N}{2} - F}{f} \times C $
where
l = lower limit of the median - class
f = frequency of the median class
N = total frequency
F = cumulative frequency of the class just before the median class
C = length of median class
Now, given, M = 25, N = 100, F = 45, C = 20 - 30 = 10, l = 20.
$\therefore $ By using formula, we have
$ 25 = 20 + \frac{50 - 45}{f} \times 10$
$ 25 - 20 = \frac{50}{f} \, \Rightarrow \, 5 = \frac{50}{f} \Rightarrow \, f = 10 $