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 inÂ finance, the range is very useful to see how big a variation or change could become.Â It is also worth mentioning that, on many occasions, the range is not a fixed measure.Â For example, let's imagine that the growth of theÂ gross domestic product (GDP)Â of a country has been between 3 and 5% during the last 20 years.Â The range for this data will be 2% but this does not mean that it will always be that.Â 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 = MaxÂ _{x}Â - MinÂ _{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.Â If we know which are the numbers with the highest and lowest value, we will only have to apply the formula.Â In Excel, for example, we can use the functions = MAX (data range) and MIN (data range).Â 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:

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

The above content published atÂ Collaborative Research GroupÂ is forÂ informational purposes onlyÂ and has been developed by referringÂ reliable sources and recommendations from experts.Â 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.