Question:

The mean deviation (correct to one decimal place) of the numbers 3, 10, 6, 11, 14, 17, 9, 8, 12 about the mean is:

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To find the mean deviation, first calculate the mean and then find the absolute deviations from the mean.
Updated On: Apr 17, 2025
  • 2.8
  • 3.1
  • 3.6
  • 4.2
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The Correct Option is B

Solution and Explanation

The numbers are: 3, 10, 6, 11, 14, 17, 9, 8, 12.
The mean of the numbers is: \[ \text{Mean} = \frac{3 + 10 + 6 + 11 + 14 + 17 + 9 + 8 + 12}{9} = \frac{90}{9} = 10 \] Now, calculate the absolute deviations from the mean: \[ |3 - 10| = 7, \quad |10 - 10| = 0, \quad |6 - 10| = 4, \quad |11 - 10| = 1, \quad |14 - 10| = 4 \] \[ |17 - 10| = 7, \quad |9 - 10| = 1, \quad |8 - 10| = 2, \quad |12 - 10| = 2 \] The sum of the absolute deviations is: \[ 7 + 0 + 4 + 1 + 4 + 7 + 1 + 2 + 2 = 28 \] The mean deviation is: \[ \frac{28}{9} \approx 3.1 \]
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