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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 mean。 The standard deviation is an 
amount calculated from the values in the sample。 Use this calculator ( 
easycalculation/statistics/standard…deviation。php) to work out the 
standard deviation by entering the numbers in your sample。 
Forecasting 
Sales drive much of a business’s activities; it determines cash flow; stock 
levels; production capacity and ultimately how profitable or otherwise a 
business will be; so; unsurprisingly; much effort goes into a。。empting to 
predict future sales。 A sales forecast is not the same as a sales objective。 An 
objective is what you want to achieve and will shape a strategy to do so。 A 
forecast is the most likely future oute given what has happened in the 
past and the momentum that provides for the business。 
The ponents of any forecast are made up of three ponents and to 
get an accurate forecast you need to depose the historic data to be。。er 
understand the impact of each on the end result: 
。 Underlying trend: This is the general direction; up; flat or down; over 
the longer term; showing the rate of change。 
。 Cyclical factors: These are the short…term influences that regularly superimpose 
themselves on the trend。 For example; in the summer months 
you would expect sales of certain products; swimwear; ice creams and 
suntan lotion; for example; to be higher than; say; in the winter。 Ski 
equipment would probably follow a reverse pa。。ern。 
。 Random movements: These are irregular; random spikes up; or down; 
caused by unusual and unexplained factors。 
Using averages 
The simplest forecasting method is to assume that the future will be more 
or less the same as the recent past。 The two most mon techniques that 
use this approach are: 
。 Moving average: This takes a series of data from the past; say the last 
six months’ sales; adds them up; divides by the number of months and 
uses that figure as being the most likely forecast of what will happen 
in month 7。 This method works well in a static; mature marketplace 
where change happens slowly; if at all。 
。 Weighted moving average: This method gives the most recent data more 
significance than the earlier data since it gives a be。。er representation of 
Quantitative and Qualitative Research and Analysis 253 
current business conditions。 So before adding up the series of data each 
figure is weighted by multiplying it by an increasingly higher factor as 
you get closer to the most recent data。 
Exponential smoothing and advanced 
forecasting techniques 
Exponential smoothing is a sophisticated averaging technique that gives 
exponentially decreasing weights as the data gets older and conversely 
more recent data is given relatively more weight in making the forecasting。 
Double and triple exponential smoothing can be used to help with different 
types of trend。 More sophisticated still are Holt’s and Brown’s linear exponential 
smoothing and Box…Jenkins; named a。。er two statisticians of those 
names; which applies autoregressive moving average models to find the 
best fit of a time series。 
Fortunately; all an MBA needs to know is that these and other statistical 
forecasting methods exist。 The choice of which is the best forecasting technique 
to use is usually down to trial and error。 Various so。。ware programs 
will calculate the best…fi。。ing forecast by applying each technique to the 
historic data you enter。 Then wait and see what actually happens and use the 
technique that’s forecast as closest to the actual oute。 Professor Hossein 
Arsham of the University of Baltimore (h。。p://home。ubalt。edu/ntsbarsh/ 
Business…stat/otherapplets/ForecaSmo。htm#rmenu) provides a useful tool 
that allows you to enter data and see how different forecasting techniques 
perform。 Duke University’s Fuqua School of Business; consistently ranked 
among the top 10 US business schools in every single functional area; 
provides this helpful link (duke。edu/~rnau/411home。htm) to all its 
lecture material on forecasting。 
Causal relationships 
O。。en; when looking at dat

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