Question

The mean deviation from the mean for the data $ 6, 7, 10, 12, 13, 4, 12, 16 $ is:

• A. 3.25
• B. 3.52
• C. 3.33
• D. 2.35

Hint:

The mean deviation is found by calculating the absolute differences between each data point and the mean, and then averaging them.

Answer 1

The Correct Option is A

Step 1: Find the mean of the data. The mean \( \mu \) is given by: \[ \mu = \frac{6 + 7 + 10 + 12 + 13 + 4 + 12 + 16}{8} = \frac{80}{8} = 10 \] Step 2: Find the absolute deviations from the mean. The absolute deviations are: \[ |6 - 10| = 4, \quad |7 - 10| = 3, \quad |10 - 10| = 0, \quad |12 - 10| = 2 \] \[ |13 - 10| = 3, \quad |4 - 10| = 6, \quad |12 - 10| = 2, \quad |16 - 10| = 6 \] Step 3: Find the mean deviation. The mean deviation is the average of these absolute deviations: \[ \text{Mean Deviation} = \frac{4 + 3 + 0 + 2 + 3 + 6 + 2 + 6}{8} = \frac{26}{8} = 3.25 \] Thus, the mean deviation from the mean is \( \boxed{3.25} \).