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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 data sets it will be apparent that there is a relationship
between certain factors。 Look at Figure 11。3。 It is a chart showing the
monthly sales of barbeques and the average temperature in the preceding
month for the past eight months。
It’s not too hard to see that there appears to be； as we might expect； a
relationship between temperature and sales； in this case。 By drawing the
line that most accurately represents the slope； called the line of best fit； we
can have a useful tool for estimating what sales might be next month； given
the temperature that occurred this month （Figure 11。4）。
The example used is a simple one and the relationship obvious and
strong。 In real life there is likely to be much more data and it will be harder
to see if there is a relationship between the ‘independent variable’； in this
254 The Thirty…Day MBA
case temperature； and the ‘dependent variable’； sales volume。 Fortunately；
there is an algebraic formula known as ‘linear regression’ that will calculate
the line of best fit for you。
There are then a couple of calculations needed to test if the relationship
is strong （it can be strongly positive or even if strongly negative it will still
be useful for predictive purposes） and significant。 The tests are known as
R…squared and the Students t…test； and all an MBA needs to know is that
they exist and you can probably find the so。。ware to calculate them on your
puter already。 Otherwise you can use Web…Enabled Scientific Services
& Applications （wessa/slr。wasp） so。。ware； which covers almost
every type of statistical calculation。 The so。。ware is free online and provided
Figure 11。4 Sca。。er diagram – the line of best fit
Figure 11。3 Sca。。er diagram example
0
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Quantitative and Qualitative Research and Analysis 255
through a joint research project w