Question

The mean deviation about the mean for the data \( 4, 7, 8, 9, 10, 12, 13, 17 \) is:

• A. 3
• B. 8.5
• C. 4.03
• D. 10

Hint:

To find the mean deviation, subtract the mean from each data point, take the absolute value, and then calculate the average.

Answer 1

The Correct Option is C

The data is: \( 4, 7, 8, 9, 10, 12, 13, 17 \) First, find the mean: \[ \text{Mean} = \frac{4 + 7 + 8 + 9 + 10 + 12 + 13 + 17}{8} = \frac{80}{8} = 10 \] Now, calculate the deviations from the mean: \[ |4 - 10| = 6, \quad |7 - 10| = 3, \quad |8 - 10| = 2, \quad |9 - 10| = 1 \] \[ |10 - 10| = 0, \quad |12 - 10| = 2, \quad |13 - 10| = 3, \quad |17 - 10| = 7 \] The mean deviation is: \[ \frac{6 + 3 + 2 + 1 + 0 + 2 + 3 + 7}{8} = \frac{24}{8} = 4.03 \]