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Question

Find the mean deviation about the mean for the following data:
6,7, 10, 12, 13,4,8, 12

Moderate

Solution

Mean of the given data is $\bar{x} = \frac{6 + 7 + 10 + 12 + 13 + 4 + 8 + 12}{8} = \frac{72}{8} = 9$
The deviations of the respective observations from the mean
$\begin{array}{l} \bar{x}, i.e., x_{i} - \bar{x} are: \\ 6 - 9, 7 - 9, 10 - 9, 12 - 9, 13 - 9, 4 - 9, 8 - 9, 12 - 9 \\ or - 3, - 2, 1, 3, 4, - 5, - 1, 3 \end{array}$
$\begin{aligned} The absolute values of the deviations, i.e., ⌊x_{i} - \bar{x} ∣ are: 3, 2, 1, 3, 4, 5, 1, 3 \end{aligned}$
The required mean deviation about the mean is:
$M.D. (\bar{x}) = \frac{\sum_{i = 1}^{8} |x_{i} - \bar{x}|}{8}$
$\begin{aligned} = \frac{3 + 2 + 1 + 3 + 4 + 5 + 1 + 3}{8} = \frac{22}{8} \\ = 2.75 \end{aligned}$

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Introduction to statistics

Remember concepts with our Masterclasses.

Find the mean deviation about the mean for the following data: 6,7, 10, 12, 13,4,8, 12

Ready to Test Your Skills?

free study material

Find the mean deviation about the mean for the following data:
6,7, 10, 12, 13,4,8, 12