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Law of Average

Is average as a metric, a good indicator for your business?

Business often use average to define different aspects, sales, inventory levels, profit margin etc. Average can be applied to almost any numerical metric and it is widely used because it is convenient and simple mathematical tool. There is however, a major flaw in using average.

Let’s take sales as a business aspect in all our example in the remainder of the article.

For example, there is small fabric company, which sells cotton yarn to major retails. As a metric of performance they are using average sales to understand the kind of requirement for inventory levels and production capacity.

The inherent flaw in using, sum of sales throughout the year and dividing it by number of month i.e. average, is the underlying assumption. Average only tells us how the sales would have been each month, had the total sales been equally distributed throughout the year.

Business owners know that this is hardly the case. In fact had it been the case, half of the business problems would have been automatically solved. Major sales are sometimes concentrated over a few months and throughout the rest of the year, the sales are sparse.

Any metric taken over a period of time forms a distribution when plotted on a graph. An average would be a suitable metric in the following case

Note how evenly distributed the sales is. However reality is something like follows.

Note how the sales increases in the festive seasons.

Statisticians use something called the standard deviation. Without understanding the mathematical intricacies of the tool, it is accurate enough to say that it determines how spread out form the arithmetic mean (average) it really is. It can also be used to measure the volatility of your sales.

Use the function STDDEV in excel to get the result.

However even standard deviation only provides partial information about your sales (in fact most of the tool does, it is only the use of a variety of tools, which gives you reliable information). But even then it should be used in addition to average since it gives a more realistic idea about your business.

An average is also an excellent choice of indicator if the distribution of sales is symmetric. For example

Mathematicians call a close cousin of what is represented in the above graph as a normal distribution.

Without getting into the mathematical significance of a normal curve there are a few things readers have already noticed.

  1. The graph is exceptionally symmetrical
  2. The graph is pivoted around the mean(average)

It is indeed proved that a normal curve is totally defined by the mean and the standard deviation (dispersion around the mean). This means given a mean and a standard deviation one can draw only one type of curve.

Coming back to the sales of a business, if your sales by anyway turns out to be normally distributed given the mean and standard deviation of your data you can predict your sales at any point of the distribution.

However, such symmetries rarely occurs in nature, even less so in business.

Hence, one of the important concepts of sampling comes in. Sample in this case has to be at least 25 in size (statistically significant) from the entire dataset of sales. If all the means of all samples are considered, then they will form a normal distribution around population mean.

Again, in this case it is the means of the samples we are considering as data for the distribution.

However such sampling is not required in daily business chores.

Another method for having a realistic idea of the distribution of any data is to divide it into quartiles or 4 parts. However in this case the data should be sorted according to time or ascending or descending order. The maximum and minimum of each quartile can give you an estimation of how the data is distributed. The mean of the entire dataset might lie somewhere away from the middle of the data.

In the above figure there is high sales in the beginning of the year. Although the average is 6.75, there are 7 months in the year where sales is below average. Hence any planning based solely on average might backfire.

This is not to discount the usefulness of average. Arithmetic mean or average is a wonderful tool of convenience and therefore can be used any point to say how well the business is doing. However, any planning or decisions should not be solely based on average. It should be scrutinized using at least 2-3 other statistical tools.

(Please note: the statistical tools described above is an introduction and most definitely doesn’t describe the mathematical intricacies behind it. It also does not represent the exhaustive list of tools used for data.

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