Question

The mean deviation about the mean for the following data:
5, 6, 7, 8, 6.9, 13, 12, 15

• A. 1.55
• B. 2.88
• C. 3.89
• D. 5

Hint:

Use absolute differences from the mean, not squares, for mean deviation. Approximate to the nearest given option if needed.

Answer 1

The Correct Option is B

First calculate the mean: $\bar{x} = \dfrac{5 + 6 + 7 + 8 + 6.9 + 13 + 12 + 15}{8} = 9.1125$
Now find the absolute deviations from the mean:
$|5 - 9.1125| = 4.1125$
$|6 - 9.1125| = 3.1125$
$|7 - 9.1125| = 2.1125$
$|8 - 9.1125| = 1.1125$
$|6.9 - 9.1125| = 2.2125$
$|13 - 9.1125| = 3.8875$
$|12 - 9.1125| = 2.8875$
$|15 - 9.1125| = 5.8875$
Sum = $25.325$
Mean Deviation = $\dfrac{25.325}{8} = 3.1656$ (approx)
Closest option using simplified method or rounding: 2.88