Multiple choice

Mean deviation of $39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45$ from their median is?

  1. $15$
  2. $1.5$
  3. $42$
  4. $35$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Data: 39, 40, 40, 41, 41, 42, 42, 43, 43, 44, 44, 45. Median is (42+42)/2 = 42. Deviations from 42: |-3|, |-2|, |-2|, |-1|, |-1|, |0|, |0|, |1|, |1|, |2|, |2|, |3|. Sum = 3+2+2+1+1+0+0+1+1+2+2+3 = 18. Mean deviation = 18 / 12 = 1.5.

AI explanation

The data contains 12 observations, so the median is the average of the 6th and 7th values; both of these values are 42, making the median 42. The absolute deviations of the 12 numbers from this median are 3, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2 and 3. The sum of these absolute deviations is 18. Dividing this sum by the total number of observations, 12, gives a mean deviation of 1.5.

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