Multiple choice

For the data set ${10, 12, 40, 35, 14, 24, 13, 21, 42, 30}$, find the mean absolute deviation to the nearest hundredth.

  1. $9.12$
  2. $11.12$
  3. $12.12$
  4. $10.12$
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D Correct answer
Explanation

First, find the mean: (10+12+40+35+14+24+13+21+42+30) / 10 = 241 / 10 = 24.1. Then, calculate the absolute deviations from 24.1: |10-24.1|=14.1, |12-24.1|=12.1, |40-24.1|=15.9, |35-24.1|=10.9, |14-24.1|=10.1, |24-24.1|=0.1, |13-24.1|=11.1, |21-24.1|=3.1, |42-24.1|=17.9, |30-24.1|=5.9. Sum of deviations = 101.2. Mean absolute deviation = 101.2 / 10 = 10.12.

AI explanation

The sum of the ten values in the data set is 241, so the mean is 24.1. The absolute differences between each value and this mean are 14.1, 12.1, 15.9, 10.9, 10.1, 0.1, 11.1, 3.1, 17.9 and 5.9, which sum to 101.2. Dividing this total by 10 yields a mean absolute deviation of 10.12.

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