Multiple choice

The mean deviation from mean of observations 5, 10, 15, 20, ......85 is

  1. $43.71$
  2. $21.17$
  3. $38.7$

  4. None of these
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B Correct answer
Explanation

Mean of 5, 10, ..., 85 (17 terms) = (5+85)/2 = 45. Mean deviation = (1/17) * sum |xi - 45|. Sum = |5-45| + |10-45| + ... + |85-45| = 40 + 35 + 30 + 25 + 20 + 15 + 10 + 5 + 0 + 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 = 360. Mean deviation = 360 / 17 = 21.176.

AI explanation

The observations form an arithmetic progression from 5 to 85 with 17 terms, so the mean is the average of the first and last terms, which is (5 plus 85) divided by 2 to equal 45. The mean deviation from the mean is the sum of absolute deviations divided by the number of terms. The absolute differences from 45 are multiples of 40 from 0 to 40, occurring as pairs, so the sum of absolute deviations is 2 times 40 times the sum of integers from 1 to 8, yielding 80 times 36 equal to 2880. Dividing 2880 by 17 terms gives approximately 21.17.

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