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Let M denote the median of the following frequency distribution. Class 0 - 4 4 - 8 8 - 12 12 - 16 16 - 20 Frequency 3 9 10 8 6 Then 20 M is equal to :

Options

  1. A416
  2. B104
  3. C52
  4. D208

Correct answer

D. 208

Step-by-step solution

( array |c|c|c| Class & Frequency & Cumulative frequency 0-4 & 3 & 3 4-8 & 9 & 12 8-12 & 10 & 22 12-16 & 8 & 30 16-20 & 6 & 36 array ) M = l + N 2 - C f h Here, N = 3 + 9 + 10 + 8 + 6 = 36 ⇒ N 2 = 18 So, median class is 8 - 12 ⇒ l = 8 , C = 22 , f = 10 , h = 4 ⇒ M = 8 + 18 - 12 10 × 4 ⇒ M = 10 . 4 ⇒ 20 M = 208

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