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。 Assign the risk in terms of uncertainty allied with each alternative。
Figure 11。1 shows an example decision tree。 The convention is that squares
represent decisions and circles represent uncertain outes。 In this example；
the problem being decided on is whether to launch a new product
or revamp an existing one。 The uncertain outes are whether the result
of the decision will be successful （￡10 million profit）； just ok （￡5 million
profit） or poor （￡1 million）。 In the case of launching a new product there is；
in the management’s best estimate； a 10 per cent （0。1 in decimals） chance
of success； a 40 per cent chance it will be ok and a 50 per cent chance it
will result in poor sales。 Multiplying the expected profit arising from each
possible oute by the probability of its occurring gives what is termed
an ‘expected value’。 Adding up the expected values of all the possible
outes for each decision suggests； in this case； that revamping an old
product will produce the most profit。
The example is a very simple one and in practice decisions are much
more plex。 We may have intermediate decisions to make； such as
should we invest heavily and bring the new product to market quickly； or
should we spend money on test marketing。 This will introduce more decisions
and more uncertain outes represented by a growing number of
‘nodes’； the points at which new branches in the tree are formed。
Quantitative and Qualitative Research and Analysis 249
If the outes of the decision under consideration are spread over several
years； you should bine this analysis with the net present value of the
monetary values concerned。 （See Discounted Cash Flow in Chapter 2；
Finance。）
Statistics
Statistics is the set of tools that we use to help us assess the truth or otherwise
of something we observe。 For example； if the last 10 phone calls a pany
received were all cancelling orders； does that signal that a business has a
problem； or is that event within the bounds of possibility？ If it is within the
bounds of possibility； what are the odds that we could still be wrong and
really have a problem？ A further issue is that usually we can’t easily examine
the entire population； so we have to make inferences from samples and；
unless those samples are representative of the population we are interested
in and of sufficient size； we could still be very wrong in our interpretation
of the evidence。 At the time of writing； there was much debate as to how
much of a surveillance society Britain had bee。 The figure of 4。2 million
cameras； one for every 14 people； was the accepted statistic。 However； a
diligent journalist tracked down the evidence to find that extrapolating a
survey of a single street in a single town arrived at that figure！
Central tendency
The most mon way statistics are considered is around a single figure
that purports in some way to be representative of a population at large。
Figure 11。1 Example decision tree
Activity
fork
Event
fork
Event
fork
Launch
new product
Revamp
old product
Successful
Successful
OK
OK
Poor
Poor
10％ （0。1）
40％ （0。4）
50％ （0。5）
30％ （0。3）
60％ （0。6）
10％ （0。10）
Expected
profit ￡s
Expected
value ￡s
10m
1m
5m
6m
4m
2m 0。2m
2。4m
1。8m
0。5m
2m
× 1m
×
×
×
×
×
=
=
=
=
=
=
3。5m
4。4m
250 The Thirty…Day MBA
There are three principal ways of measuring tendency and these are the
most o。。en confused and frequently misrepresented set of numbers in the
whole field of statistics。
To analyse anything in statistics you first need a ‘data set’ such as that in
Table 11。1。
Table 11。1 The selling prices of panies’ products
Product Selling price ￡s
1 30
2 40
3 10
4 15
5 10
The mean （or average）
This is the most mon tendency measure and is used as a rough and
ready check for many types of data。 In the example above； adding up the
prices – ￡105 and dividing by the number of products – 5； you arrive at a
mean； or average； selling price of ￡21。
The median
The median is the value occurring at the centre of a data set。 Recasting the
figures in Table 11。1 puts product 4’s selling price of ￡15 in that position；
with two higher and two lower prices。 The median es into its own in
situations where the outlying values in a data set are extreme； as they are
in our example； where in fact most of the products sell for well below ￡21。
In this case the median would be a be。。er measure of the central tendency。
You should always use the median when the distribution is skewed。 You
can use either the mean or the median when the population is symmetrical
as they will give very similar results。
The mode
The mode is the observation in a data set appearing the most o。。en； in this
example it is ￡10。 So if we were surveying a sample of the customers of the
pany in this example； we would expect more of them to say they were
paying ￡10 for their products； though； as we know； the average price is
￡21。
Quantitative and Qualitative Research and Analysis 251
Variability
As well as measuring how values cluster around a central value； to make
full use of the data set we need to establish how much those values could
vary。 The two most mon methods employed are the following。
Range
The range is calculated as the maximum figure minus the minimum figure。
In the example being used here； that is ￡40 – ￡10 = ￡30。 This figure gives
us an idea of how dispersed the data is and so how meaningful； say； the
average figure alone might be。
Standard deviation from the mean
This is a rather more plicated concept as you need first to grasp the
central limit theorem； which states that the mean of a sample of a large
population will approach ‘normal’ as the sample gets bigger。 The most
valuable feature here is that even quite small samples are normal。 The
bell curve； also called the Gaussian distribution； named a。。er Johann Carl
Friedrich Gauss （1777–1855）； a German mathematician and scientist； shows
how far values are distributed around a mean。 The distribution； referred to
as the standard deviation； is what makes it possible to state how accurate
a sample is likely to be。 When you hear that the results of opinion polls
predicting elections based on samples as small as 1；000 are usually reliable
within four percentage points； 19 times out of 20； you have a measure of
how important。 （You can get free tutorials on this and other aspects of
statistics at Web Interface for Statistics Education （h。。p：//wise。cgu。edu）。）
Figure 11。2 is a normal distribution that shows that 68。2 per cent of
the observations of a normal population will be found within 1 standard
Figure 11。2 Normal distribution curve （bell） showing standard deviation
Mean
–3 SD –2 SD –1 SD 0 ＋1 SD ＋2 SD ＋3 SD
2。1％ 2。1％
13。6％ 13。6％
34。1％ 34。1％
252 The Thirty…Day MBA
deviation of the mean； 95。4 per cent within 2 standard deviations； and
99。6 per cent within 3 standard deviations。 So almost 100 per cent of the
observations will be observed in a span of six standard deviations； three
below the mean and three above the mea