What is the mean deviation of eight observations?

6, 7, 10, 12, 13, 4, 8, 12

Correct option is A

Given:

The observations are:
6, 7, 10, 12, 13, 4, 8, 12

We are asked to find the mean deviation of these observations.

Formula Used:

Mean Deviation =$$\frac{\sum |x_i - \bar{x}|}{n}$$​

Where:

​$$x_i$$ are the individual observations,

​$$\bar{x}$$ is the mean of the observations,

n is the number of observations.

Solution:

The sum of the observations is:

6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72

There are 8 observations, so the mean is:

​$$\bar{x} = \frac{72}{8} = 9$$​​​​

|6 - 9| = 3

|7 - 9| = 2

|10 - 9| = 1

|12 - 9| = 3

|13 - 9| = 4

|4 - 9| = 5

|8 - 9| = 1

|12 - 9| = 3

The sum of the absolute deviations is:

3 + 2 + 1 + 3 + 4 + 5 + 1 + 3 = 22

Mean Deviation = $$\frac{22}{8} = 2.75$$​