Finding the Mean of a Symmetric Distribution

Symmetrical distribution is a situation in which the values of variables occur at regular frequencies, and the mean, median and mode occur at the same point. Unlike asymmetrical distribution, symmetrical distribution does not skew.

Find the mean of the following symmetric distribution.

1, 1, 4, 4, 5, 6, 7, 7, 10, 10

Solution

Step 1:

Mean of distribution = $\frac{(1 + 1 + 4 + 4 + 5 + 6 + 7 + 7 + 10 + 10)}{10} = \frac{55}{10}$ = 5.5

Step 2:

Or mean of middle two numbers = $\frac{(5+6)}{2}$ = 5.5

So mean of symmetric distribution = 5.5

Find the mean of the following symmetric distribution.

2, 2, 4, 4, 5, 6, 7, 7, 9, 9

Solution

Step 1:

Mean of distribution = $\frac{(2 + 2 + 4 + 4 + 5 + 6 + 7 + 7 + 9 + 9)}{10} = \frac{55}{10}$ = 5.5

Step 2:

Or mean of middle two numbers = $\frac{(5+6)}{2}$ = 5.5

So mean of symmetric distribution = 5.5