Multiple choice

Calculate Mean deviation about median for the given data Marks $100-110$ $110-120$ $120-130$ $130-140$ $140-150$ Frequency $4$ $6$ $5$ $3$ $2$

  1. $10.5$
  2. $31.5$
  3. $12.5$
  4. $66.16$
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A Correct answer
Explanation

First, find the median class by cumulative frequency. Total frequency is 20, so median is at 10th value, which falls in 110-120. Median = 110 + ((10-4)/6)10 = 120. Mean deviation about median = sum(f|x-median|) / sum(f). Midpoints are 105, 115, 125, 135, 145. Deviations are 15, 5, 5, 15, 25. MD = (4*15 + 6*5 + 5*5 + 3*15 + 2*25) / 20 = (60 + 30 + 25 + 45 + 50) / 20 = 210 / 20 = 10.5.

AI explanation

The total frequency is 20, so the median corresponds to the average of the 10th and 11th values. The cumulative frequencies are 4, 10, 15, 18, and 20, meaning both the 10th and 11th values fall in the 110-120 interval, making the median 115. The sum of absolute deviations from the median is |105 - 115|*4 + |115 - 115|*6 + |125 - 115|*5 + |135 - 115|*3 + |145 - 115|*2, equaling 210. Dividing 210 by 20 gives a mean deviation of 10.5.

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