Multiple choice

The mean deviation from the data $3, 10, 10, 4, 7, 10, 5$.

  1. $3$
  2. $2$
  3. $3.75$
  4. $2.57$

  5. None of these
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D Correct answer
Explanation

First, find the mean: (3+10+10+4+7+10+5) / 7 = 49 / 7 = 7. Then, calculate the absolute deviations from the mean: |3-7|=4, |10-7|=3, |10-7|=3, |4-7|=3, |7-7|=0, |10-7|=3, |5-7|=2. The mean of these deviations is (4+3+3+3+0+3+2) / 7 = 18 / 7 = 2.57.

AI explanation

The formula for mean deviation is the sum of absolute deviations from the mean divided by the number of observations. First, find the mean of the data 3, 10, 10, 4, 7, 10, 5 by adding them to get 49 and dividing by 7, resulting in a mean of 7. The absolute deviations from the mean are 4, 3, 3, 3, 0, 3, and 2, which sum to 18. Dividing the total deviation of 18 by the 7 observations gives a mean deviation of approximately 2.57.

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