A quartile is one of four equal groups into which a data set can be divided according to the distribution of values of a particular variable. As Wikipedia explains, there are three different accepted methods with which to calculate quartiles. If there are an even number of data points in the data set, all three different methods give the same value for quartiles. If there are an odd number of data points, these methods can provide a different value depending on data sets. In certain scenarios, these differences across the methods may be significant in your decision making. This can make it confusing if you are trying to verify the statistics behind the analytics in Sniffie by yourself.

Here at Sniffie, we pride ourselves in the quality and statistical correctness of all our data and analytics. Thus, I felt it was necessary to write this article and provide information on how the quartiles (and quantiles) are calculated and the reason for us selecting one method out of the three outlined in the above Wikipedia article.

Furthermore, let's all hope that one day, there is a standard method for calculating these values. Already in 1996 some statisticians have argued such a standard should be chosen by the statistics community for discrete distributions, but alas, it has not yet happened. Maybe it will happen one day.

Text below describing the quartile calculation methods is directly cited from this article on Wikipedia on 31st July, 2019.

Method 1:

Method 2:

Method 3:

1st quartile (Q1), by mathematical definition, is the 25th percentile and falls exactly in the 1/4 point in the data set. In an even number data set, that 1/4 point falls exactly between two points in an even data set and Q1 has, by definition, only a one single value.
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Let's consider the following set of numbers (Dataset A): 1, 1, 8, 12, 13, 13, 14, 16, 19, 22, 27, 28, 31.

There are 13 items in Dataset A. Now the 1/4 point of the data set does not fall between two points. Rather, it falls nearer one point than any other, but it also does not fall exactly on any of the points either. This is the cause for the differences in the values the calculation methods provide.

In Dataset A, the different methods for calculating quartiles provided in the Wikipedia article above are as follows:

As you can see, the difference in minor but there is still a difference. Method 2 is used in e.g. Microsoft Excel, Google Sheets and Python's NumPy library in quartile calculation. Method 1 is used by may online tools when calculating quartiles. Method 3 is used in e.g. Wolfram Alpha computational engine.

In total, there are actually 9 different ways of calculating quantiles (quartiles are 4-quantiles), which means that there may be actually 9 different outcomes for the Q1 value. For Dataset A, these are: 12, 12, 8, 9, 11, 10, 12, 10.667, 10.75

Here at Sniffie, we use Method 2 in calculating quartiles (and quantiles). We chose these because of the following reasons: