Histograms are an excellent way of showing
the variation graphically. However if
we are to compare processes and evaluate
improvements or changes objectively we
need a hard number.
The measure that is almost invariably
chosen is the 'standard deviation'. It
is easiest to start by explaining the
variance, which is just the square of
the standard deviation.
I'll explain how to calculate it first
and then explain how it works. The formula
for the variance is:
Notice that it uses similar notation
to the formula for the mean. It looks
more forbidding and I’ll go through the
calculation with a small sample of numbers:
The mean is 4:
| 1)
The Index |
2)
The Data
|
3)
The Mean |
4)
The difference between the data
values and the mean |
5)
The square of column (4)
|
| 
|
|
|
|
|
| 1
|
1 |
4
|
-3 |
+9
|
| 2
|
2 |
4 |
-2
|
+4
|
| 3
|
3 |
4 |
-1
|
+1
|
| 4
|
6 |
4 |
+2
|
+4
|
| 5
|
8 |
4 |
+4 |
+16 |
| |
|
|
|
34 |
There are five data values 'n'. The variance
is obtained by dividing by 'n-1'
 |
The times taken to repair equipment
breakdowns, in hours, over the
past week were as follows:
What was the
variance of the repair time?
|
| |
