Multiple choice

$x_i$ $3$ $5$ $7$ $9$ $11$ $13$ $f_i$ $6$ $8$ $15$ $25$ $8$ $4$ Find the Mean Deviation (M.D) about the mean

  1. $2.1$
  2. $2.25$
  3. $2.09$
  4. $2.71$
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C Correct answer
Explanation

Mean = sum(f*x)/sum(f) = (18+40+105+225+88+52)/66 = 528/66 = 8. Mean deviation = sum(f*|x-mean|)/sum(f) = (6*|3-8| + 8*|5-8| + 15*|7-8| + 25*|9-8| + 8*|11-8| + 4*|13-8|)/66 = (30+24+15+25+24+20)/66 = 138/66 = 2.0909.

AI explanation

The total frequency is 6 + 8 + 15 + 25 + 8 + 4, which equals 66. The sum of the products of values and frequencies is 18 + 40 + 105 + 225 + 88 + 52, which equals 528, giving a mean of 528 divided by 66, or 8. The absolute deviations from this mean are 5, 3, 1, 1, 3 and 5; multiplying these by their respective frequencies gives 30, 24, 15, 25, 24 and 20. The sum of these products is 138; dividing by the total frequency of 66 yields a mean deviation of 2.09.

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