Page 176 - BA2 Integrated Workbook - Student 2017

Chapter 11

5.2 Standard deviation and variance

The standard deviation is a way of measuring how far away on average the data
points are from the mean. In other words, they measure average variability about the
mean. As such standard deviation is often used with the mean when describing a
data set.

For example, suppose a data set has just two observations: 10 and 30. The mean
here is 20 and the standard deviation will be 10 as both observations are 10 units
away from the mean.

Calculating the standard deviation involves the following steps:

1 Look at the difference between each data value and the mean

2 To get rid of the problem of negative differences cancelling out positive ones,
square the results

3 Work out the average squared difference (this calculates the variance)

4 Take the square root to get the standard deviation

The formula for the standard deviation is:

∑( − ̅)
=

or

∑fx 2 ∑fx 2
s= -
∑f ∑f

The variance is simply the standard deviation squared

Note: the mathematical symbol used to denote standard deviation is σ.

Go through illustration 17

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