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


  • 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 144,347
Month 212,445
Month 326,880
Month 423,366
Month 542,464
Month 615,480
Month 721,562
Month 811,625
Month 939,496
Month 1039,402
Month 1147,699
Month 1244,315
Month 1329,581
Month 1444,320
Month 1535,264
Month 1610,124
Month 1743,520
Month 1826,360
Month 1919,534
Month 2030,755
Month 2137,327
Month 2215,832
Month 2333,919
Month 2429,498
Month 2546,136
Month 2618,007
Month 2736,339
Month 2827,696
Month 2947,413
Month 3047,636
Month 3120,978
Month 3249,079
Month 3340,668
Month 3445,932
Month 3540,454
Month 3646,132
Month 3735,054
Month 3811,906
Month 3922,532
Month 4043,045
Month 4145,074
Month 4216,505
Month 4327,336
Month 4437,831
Month 4529,757
Month 4637,765
Month 4722,237
Month 4838,601

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.

The above content published at Collaborative Research Group is for informational purposes only and has been developed by referring reliable sources and recommendations from experts. We do not have any contact with official entities nor do we intend to replace the information that they emit.
Luke is passionate about fostering student involvement and connection. He studied psychology for his major and likes learning about the past. Luke aims to specialize in artificial intelligence and cybersecurity.


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