Multiple choice

$x_i$ $3$ $5$ $7$ $9$ $11$ $13$ $f_i$ $6$ $8$ $15$ $3$ $8$ $4$ Find the Mean Deviation (M.D) about the median.

  1. $2.32$
  2. $2.12$
  3. $2.65$
  4. $2.73$
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A Correct answer
Explanation

First, find the median of the frequency distribution. The total frequency is 54, so the median is the value corresponding to the 27th and 28th observation, which is 7. Calculate the mean deviation about 7 using the formula sum(f_i * |x_i - median|) / sum(f_i).

AI explanation

First, calculate the cumulative frequencies, which are 6, 14, 29, 32, 40 and 44. Since the total frequency is 44, the median corresponds to the average of the 22nd and 23rd values, both of which fall in the class with a frequency of 15, making the median 7. The absolute deviations from the median are 4, 2, 0, 2, 4 and 6; multiplying these by their respective frequencies gives 24, 16, 0, 6, 32 and 24. The sum of these products is 102; dividing by the total frequency of 44 gives a mean deviation of 2.32.

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