Project Management – Statistics for Dummies (part 2)

The first part of this series (Project Management – Statistics for dummies (part 1)) focused on the meaning of the Mean, Median and the Mode.

Today’s installment will try to make sense of the Variance and the Standard Deviation.

The Variance

The variance is a measure of how spread out a data distribution is. It is computed as the average squared deviation of each number from its mean. Sounds a bit complicated so let’s try and work it out.

070410 0140 ProjectMana12 Project Management – Statistics for Dummies (part 2)

Using mathematical symbols, the above equation will look as follows:

070410 0140 ProjectMana22 Project Management – Statistics for Dummies (part 2)

Where:

is the Variance
X refers to each of the individual items in the set of values
µ is the Mean
N is the number of items in the set

For example:

A project schedule consists of 10 tasks, with the following estimated durations:

Task ID	Estimated Duration (days)
1	3
2	4
3	5
4	6
5	3
6	7
7	4
8	5
9	2
10	4

Based on the above:

Sum of all data values = 3 + 4 + 5 + 6 + 3 + 7 + 4 + 5 + 2 + 4 = 43 days
Number of data values = 10
The mean = 43 / 10 = 4.3 days

Now let’s calculate the Variance:

The sum of the squares of the difference between the individual values and the Mean =

(3 – 4.3)²+ (4 – 4.3)²+ (5 – 4.3)²+ (6 – 4.3)²+ (3 – 4.3)²+ (7 – 4.3)²+ (4 – 4.3)²+ (5 – 4.3)²+ (2 – 4.3)²+ (4 – 4.3)²= 22.333

With N = 10 the Variance = 22.33 / 10 = 2.2333

The Standard Deviation

The Standard Deviation (– pronounced Sigma) is the square root of the Variance which, in the example above will be 070410 0140 ProjectMana4 Project Management – Statistics for Dummies (part 2) = 1.494434

So what does it actually mean?

Like the Variance, the Standard Deviation is a measure of how spread out a data distribution is around the mean (average) of the set. While the mean only provides an indication of the average result, it lacks the ability to indicate how widely spread all items in the set are. The Standard Deviation provides this additional dimension by indicating how spread the data items are from the average. A set of values that are closely clustered near the mean will have a low standard deviation, a set of numbers that are widely separated will have a higher standard deviation and a set of numbers that are all the same will have a standard deviation of zero.

Standard Deviation and Project Uncertainty

The Program Evaluation and Review Technique (PERT) stipulates the use of Standard Deviation as a reflection of each tasks estimation’s uncertainty as it is calculated as the difference between the pessimistic and optimistic duration divided by six. A small Standard Deviation would be interpreted as a smaller uncertainty compared with a larger Standard Deviation. It should be noted, however, that although it would be theoretically correct to determine the level of uncertainty for each task by determining the tasks’ duration Standard Deviation; determining the project’s standard deviation require a more rigor approach which will involve the use of “Monte Carlo Simulation“.

Interested to explore this topic a bit further? – check out the following books