Statistics

Range (Statistics)

What will you find in this article?

The range is a numerical value that indicates the difference between the maximum and minimum value of a population or statistical sample.

The range is usually used to obtain the total dispersion. That is, if we have a sample with two observations: $10 and $100, the range will be $90.

Especially in finance, the range is very useful to see how big a variation or change could become. It is also worth mentioning that, on many occasions, the range is not a fixed measure. For example, let’s imagine that the growth of the gross domestic product (GDP) of a country has been between 3 and 5% during the last 20 years. The range for this data will be 2% but this does not mean that it will always be that. So if in year 21, the growth is -1%, the range of the last 21 years, will go from 2% to 6%.

It is also known as a statistical tour.

Range formula

To calculate the range of a sample or statistical population we will use the following formula:

R = Max x – Min x

Where

  • R is the range.
  • Max is the maximum value of the sample or population.
  • Min is the minimum value of the sample or statistical population.
  • x is the variable on which this measure is to be calculated.

For this, it is not necessary to order the values from highest to lowest or vice versa. If we know which are the numbers with the highest and lowest value, we will only have to apply the formula. In Excel, for example, we can use the functions = MAX (data range) and MIN (data range). From the cell that contains MAX we subtract the cell that contains MIN and get the range.

Example of rank in statistics

Suppose we have a company that produces microphones and then sells them to major computer brands. This company entrusts an economist to carry out a study on the evolution of sales (last 4 years) to, later, offer advice that improves business results. Among many other metrics, the microchip production range is required to be calculated. Below is the following data table:

Month 1 44,347
Month 2 12,445
Month 3 26,880
Month 4 23,366
Month 5 42,464
Month 6 15,480
Month 7 21,562
Month 8 11,625
Month 9 39,496
Month 10 39,402
Month 11 47,699
Month 12 44,315
Month 13 29,581
Month 14 44,320
Month 15 35,264
Month 16 10,124
Month 17 43,520
Month 18 26,360
Month 19 19,534
Month 20 30,755
Month 21 37,327
Month 22 15,832
Month 23 33,919
Month 24 29,498
Month 25 46,136
Month 26 18,007
Month 27 36,339
Month 28 27,696
Month 29 47,413
Month 30 47,636
Month 31 20,978
Month 32 49,079
Month 33 40,668
Month 34 45,932
Month 35 40,454
Month 36 46,132
Month 37 35,054
Month 38 11,906
Month 39 22,532
Month 40 43,045
Month 41 45,074
Month 42 16,505
Month 43 27,336
Month 44 37,831
Month 45 29,757
Month 46 37,765
Month 47 22,237
Month 48 38,601
MAXIMUM 49,079
MINIMUM 10,124
RANK 38,955

The month with the most microphones produced by the company (MAXIMUM) was month 32 with 49,079 microphones produced. For its part, the moment with the least microphones produced took place in month 16 with 10,124 microphones produced. Therefore, the statistical range that is the difference (49,079-10,124) stands at 38,955.

How is this interpreted? This means that during the last 4 years the maximum variation that has occurred has been 38,955 microphones produced. Graphically we can see it as follows:

Range in statistics example graph

The green point is the maximum, the red point the minimum, and the yellow dotted line to the right is the difference. That is, the range.

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