Range (Statistics): What is it, definition and concept

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:

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.