Marketers often hear the term ‘Standard Deviation’ during research debriefs, and conversations with operational personnel managing quality. Many do not know what the term means, and in what context to use it.
Standard Deviation is a statistical term that measures the variation in a set of values from the mean, or average of that set of values. The greater the standard deviation, the greater will be the spread of the data from its mean. In effect, it gives you a level of confidence in the conclusions drawn from the data.
Those values can be anything, from the time it takes for you to travel to work each day, to the variation in the size or weight of a widget coming off a production line, or indeed, from any individual part of that production line.
Take your pre-covid commute as an example. You live in Artarmon, 10km’s from your Sydney CBD office. The drive can take anything from 15 minutes to 110 minutes. If you recorded the time taken for a period, say 3 months, assuming you worked every weekday, you would have 130 data points of the time it took to make the commute, to and from work. Assume you took an average of those times, and it was 30 minutes. The Standard Deviation calculation ‘translated’ means that in 68.2% of the commutes, your travel time would be within one standard deviation of the mean of 30 minutes, and 95.4% of the commutes would be within two standard deviations of the mean of 30 minutes.
Let us assume the distribution of the data points led to a calculation of one standard deviation being 7 minutes. In other words, 68.2% of the time you would complete the trip between 23 and 37 minutes. That calculation also results in 2 standard deviations being 17 minutes, meaning that 95.4% of the time you made the commute between 47 and 13 minutes.
Those ‘outliers’ falling outside two standard deviations will be unusual situations. You went into work at 2.00am for a conference call overseas, and you got to the office in 10 minutes, and one morning, there was a ‘prang’ on the bridge, and it took over 2 hours to make the journey. These would be the journeys that made up the very unusual data points in the set, out at 3 standard deviations, within which 99.7% of journeys fell, or further.
This might seem a bit quantitative for many marketers, but if you are to be taken seriously in the boardroom, you need to be able to speak ‘Data’ the language of the boardroom. The typical marketing type assurances based on opinion and theory must be at least partly replaced by the quantitative language of the boardroom.
For those looking for a bit more, there are plenty of resources on the web, and there is a SD formula in Excel which leads you through the steps to do the calculation. However, in principle, the calculation has a few steps:
- Calculate the square of the differences between all the data points, and the mean, then add them up.
- Divide that sum by the sample size minus1, which gives you the variance. The variance is a statistical picture of how spread out the data points in the set are.
- Calculate the square root of the variance, to give the Standard deviation.
As a marketer, you do not have to know the formula, but you absolutely must understand what the term ‘standard deviation’ means, and where it is best used. It might be useful to ‘fiddle’ with the formula in Excel.
Header graph from Wikipedia.
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