Finding the Mean From an Assumed Mean

In this worksheet, we will learn how to find the mean from an assumed mean.

Example

Find the mean of 10 numbers.
50.5, 50.7, 52.1, 53.5, 54.0, 56.9, 58.8, 59.1, 59.3, 59.8

Method

First take a guess at what the mean could be, 54.0 perhaps.

Then work out the deviations of each value from 54.0

50.5 - 54.0 = -3.5
50.7 - 54.0 = -3.3
52.1 - 54.0 = -1.9
53.5 - 54.0 = -0.5
54.0 - 54.0 = 0
56.9 - 54.0 = 2.9
58.8 - 54.0 = 4.8
59.1 - 54.0 = 5.1
59.3 - 54.0 = 5.3
59.8 - 54.0 = 5.8

Add the deviations to get 14.7

Share the deviations among the 10 values 14.7 ÷ 10 = 1.47

Add this on to the assumed mean.

Mean = 54.0 + 1.47 = 55.47