Question

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

• A. 3
• B. 24
• C. 10
• D. 8

Hint:

The mean deviation is the average of the absolute differences between each data point and the mean. It gives an idea of how spread out the data is around the mean.

Answer 1

The Correct Option is A

Step 1: First, find the mean of the given data. The data set is: \( 4, 7, 8, 9, 10, 12, 13, 17 \). The mean \( \bar{x} \) is calculated as: \[ \bar{x} = \frac{4 + 7 + 8 + 9 + 10 + 12 + 13 + 17}{8} = \frac{80}{8} = 10. \] Step 2: Now, calculate the absolute deviations from the mean: \[ |4 - 10| = 6, \quad |7 - 10| = 3, \quad |8 - 10| = 2, \quad |9 - 10| = 1, \] \[ |10 - 10| = 0, \quad |12 - 10| = 2, \quad |13 - 10| = 3, \quad |17 - 10| = 7. \] Step 3: Find the mean of these absolute deviations: \[ {Mean Deviation} = \frac{6 + 3 + 2 + 1 + 0 + 2 + 3 + 7}{8} = \frac{24}{8} = 3. \] Thus, the mean deviation about the mean is 3.