Multiple choice

Find the mean deviation about the mean of the following data: $15,17,10,13,7,18,9,6,14,11$.

  1. $3.1$
  2. $3.2$
  3. $3.3$
  4. $3.4$
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D Correct answer
Explanation

Data: 15, 17, 10, 13, 7, 18, 9, 6, 14, 11. Sum = 120. Mean = 12. Deviations: |15-12|=3, |17-12|=5, |10-12|=2, |13-12|=1, |7-12|=5, |18-12|=6, |9-12|=3, |6-12|=6, |14-12|=2, |11-12|=1. Sum of deviations = 3+5+2+1+5+6+3+6+2+1 = 34. Mean deviation = 34/10 = 3.4.

AI explanation

First, find the mean of the 10 numbers, which is 120 divided by 10, or 12. Next, calculate the absolute values of the deviations from this mean: 3, 5, 2, 1, 5, 6, 3, 6, 2 and 1. Adding these absolute deviations gives a total of 34. Divide this sum by the total number of observations, 10, to get the mean deviation about the mean, which is 3.4.

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