Before I go ahead with describing some basic terms in statistics, I would underline that I am not actually a statistician, however, hope that I have yielded adequate guidance below to throw light on particular terms. This article describes a couple of standard statistics terms and tries to stretch these with a little comment on just how they may be made use of in practice. The use of statistics in the management of risk is enormous and it is not the intention below to provide genuine illustrations in this area but to make certain that you acquire some idea of their essential meaning.
Mean (expected value or average):
We could take any activity and measure values that summarize that event. Let us say that we measure 12 values, they could be:
Values: 3, 5, 5, 6, 7, 9, 10, 11, 12, 12, 15, 16
The total of these values is: 111
The total number of values is: 12
It follows that, clearly the mean will be 111 divided by 12 = 9.25
Hence:
(3 + 5 + 5 + 6 + 7 + 9 + 10 + 11 + 12 + 12 + 15 + 16) / 12 = 111/12 = 9.25
This value of 9.25 is the 'expected value' which you might anticipate from measuring a single value for the activity, but undoubtedly, in practice there is a spectrum of values. These 'expected values' are additive.
If we had 4 particular events and we got comparable measurements for each we might just finish up with 'expected values' for each event of:
5.3, 8.4, 6.3 and 11.3
If we then took into account the result of measuring the outcome of the 4 events we might just anticipate a total value of:
(5.3 + 8.4 + 6.3 + 11.3) = 31.3
Once again, the true value will be in a range.
Likelihood:
We made reference earlier to an event in which we collected the following values:
Values: 3, 5, 5, 6, 7, 9, 10, 11, 12, 12, 15, 16
If we were to anticipate an event with these values we will be assuming that they are all just as likely for the calculation of the 'expected value' or the mean. Simply put if there is little possibility of the initial six values being measured, then only the final 6 matter, therefore the 'expected value' would be:
(10 + 11 + 12 + 12 + 15 + 16) / 6 = 76/6 = 12.7
And so, in practice not only is there a distribution of values, their likelihood of occurring may equally be different.
We may take a simple look at a task in a project. We may wish to understand by how much time it could be postponed before it starts. A project manager can call upon the expert for his help and he might suggest 16 weeks. The project manager can take advantage of this guidance with regard to his planning. Nevertheless, this estimation will be based upon certain assumptions which the project manager should challenge.
If the expert is 100 % positive that there will be 16 weeks hold up that's very good, but it is not often the case. What we do appreciate is that there will be a setback. The chance of this happening is 1, i.e, it will take place. We could, now, think of other probable circumstances.
Let us suppose that we possess a range of hold ups (in working weeks) each one with a distinct likelihood. We may have:
(Delay)..........(Probability)..........(Contribution)
6.........................0.3......................6 x 0.3 = 1.8
16.......................0.5.....................16 x 0.5 = 8.0
20.......................0.2.....................20 x 0.2 = 4.0
The 'contribution' reflects a 'weighted' value. Note that the total of each of the chances adds up to 1, which will be the chance of the hold up actually happening.
The expected value this time becomes:
(1.8 + 8.0 + 4.0) = 13.8 weeks
This is the more probable value which the project manager might make use of in his plans rather than 16 weeks.
Supposing that we assessed a set of 4 comparable activities we might finish up with a total delay of 13.8 x 4 = 55.2 weeks (if carried out one after the other and not at the same time). If we had taken an isolated estimate of 16 working weeks the potential total hold up to the project would have come to 64 weeks (almost 16 % longer).
Whilst evaluating a single activity the effect is not too much of a problem, however, when evaluating multiple activities the differences can certainly accumulate.
The value of 16 weeks hold up becomes the most likely (highest chance) and is 2.2 weeks more than the 13.8 working weeks above.
This is because the distribution of the values is 'skewed' a little. Had there existed a balanced spread the 'expected value' would have calculated as coincidng with as the original estimate, that is, 16 weeks.
(Delay)..........(Probability)..........(Contribution)
12......................0.25......................12 x 0.25 = 3.0
16......................0.5........................16 x 0.5 = 8.0
20......................0.25.......................20 x 0.2 = 5.0
Above the contributions are:
(3.0 + 8.0 + 5.0) = 16 working weeks
I hope, the above information has provided a little understanding into one of the basic terms in statistics, the 'mean' of a set of values'.
Look out for additional terms in future articles.
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