PMP module book final.pdf - Blackboard - University of Leicester

PROFESSIONAL MANAGEMENT PROJECT
The sum then needs to be scaled in some way to take account of the number of
observations (5):
40/5 = 8
When this is done, the measure that results is called the variance. The question then
arises as to what units the variance is measured in. Since the deviations were squared
in the course of the calculations, the answer must be that these are now in squared
units. This is a somewhat difficult concept to grapple with, so we return to ordinary
units by taking the square root of the variance, to obtain the standard deviation.
The square root is the value which, multiplied by itself, produces the value you began
with, and can be arrived at using even the most basic calculator. Just enter the value
then press the √ key. With a variance of 8, the square root would be 2.82.
The standard deviation is explained succinctly by Rowntree (1981:53–54) as follows:
“If there were no dispersion at all in a distribution, all the observed values
would be the same. The mean would also be the same as this repeated
value. No observed value would deviate or differ from the mean. But,
with dispersion, the observed values do deviate from the mean, some
by a lot, some by only a little. Quoting the standard deviation of a
distribution is a way of indicating a kind of ‘average’ amount by which
all of the values deviate from the mean. The greater the dispersion, the
bigger the deviations and the bigger the standard (average) deviation.”
Two measures have thus been presented that can be used to summarise a distribution
or to compare different distributions; the mean and the standard deviation.
The standard deviation can also be used to compare individual observations from two
distributions. Suppose there are two groups of students studying the same module.
The module assignment for each group is set and marked by different members of
academic staff, but there is only one prize to award to the best student overall. Should
it be awarded to the best student in Group 1 or Group 2? It would be unfair simply to
take the student with the highest mark, since one assignment could be more difficult
than the other, the marking more severe in one case, or different marking scales may
have been used.
One solution would be to give the prize to the student who has done best relative to
his or her own group. This could be measured by the number of standard deviations
each student’s mark is above or below the mean of their group. Only the marks of
the best student in each group would have to be used, so the calculation is fairly
straightforward:
69 – 60 = 1.5 55 – 50 = 2.0
6 2.5
(Group 1) (Group 2)
108 SChOOL OF MANAGEMENT