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2.4 Descriptive Statistics – Variability
The measure of center is always a good start. But what does a sample mean not tell us It fails to
describe how far apart the data are from one another. In other words, we need to assess the
variability of variance of the numbers we have collected.
The simplest way we might go about describing the variability is by simply looking at the range
of the data, such that:
Range = largest observation - smallest observation
Albeit, this still does not help us identify how spread out the data are. For example, suppose we
find our range to be 100 units (see dataset below). This might seem rather daunting at first, but
what if all values were clumped between 0 and 10, and there existed an outlier of 110
Obviously, this range is often determined by outliers alone.
0 1 3 10 8 7 4 110
2.4.1 Standard Deviation
To create a better measure of variability that takes all data points into account, just like the mean
does, statisticians established a standard deviation. As the title implies, this is a standard tool
that measures the average deviations (or by how much each values deviates) from the mean. This
requires us to find all the deviations for points in our dataset,
We would find all of these. Let‟s demonstrate with the above dataset:
Value
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0 -17.875
1 -16.875
3 -14.875
10 -7.875
8 -9.875
7 -10.875
4 -13.875
110 92.125
Mean: 17.875
The deviations that we observe to be below the mean produce a negative deviation and the one
above the mean has a positive deviation. To find an average deviation, we would ideally add
Statistics for Decision-Making in Business © Milos Podmanik Page 67