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· 28 Nov 2021

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What is the range mathematics

In statistics and mathematics, the range is the difference between the maximum and minimum values ​​of a data set and serves as one of the two important characteristics of a data set. The formula for a range is the maximum value minus the minimum value in the dataset, which allows statisticians to better understand how diverse the dataset is.

Two important features of a data set include the data center and the data dissemination, and the center can be measured in several ways: the most popular of these are mean, median, function, and middle class, but similarly, there are different ways of calculating how the data set is propagated and the easiest and most absolute measure of propagation is called amplitude.
Range calculation
Calculating the range is very simple. All we have to do is find the difference between the highest data value in our total and the lowest data value. In summary, we have the following formula: Range = Maximum value - Minimum value. For example, the data set 4,6,10, 15, 18 has a maximum of 18, at least 4, and a range of 18-4 = 14.

Range restrictions
The range is a very raw measure of data spread because it is extremely sensitive to extreme values, and therefore, there are some limitations to the usefulness of a true range of a data set in statisticians because a data value can affect the value of the range.

For example, consider the data set 1, 2, 3, 4, 6, 7, 7, 8. The maximum value is 8, the minimum is 1, and the region is 7. Next, consider the same data set, with only the value 100 is included. The range now becomes 100-1 = 99 where the addition an additional data points significantly affected the value of the range. The standard deviation is another propagation measure that is less sensitive to extreme values, but the disadvantage is that the calculation of the standard deviation is much more complicated.

The range tells us nothing about the internal features of our data set. For example, consider the data set 1, 1, 2, 3, 4, 5, 5, 6, 7, 8, 8, 10 where the range of this data set is 10-1 = 9. If we then compare this with the data set 1, 1, 1, 2, 9, 9, 9, 10. Here, the range is, once again, nine, however, for this second set and in contrast to the first set, the data is gathered around the minimum and maximum. Other statistics, such as the first and third quadrants, should be used to detect some of this internal structure.

Range applications
The range is a good way to get a very basic understanding of how numbers are scattered in the data set, as it is easy to calculate, and it requires only a basic numeric function, but there are also some other applications of the range of a data set in statistics.

The range can also be used to estimate another measure of propagation, the standard deviation. Instead of going through a rather complicated formula to find the standard deviation, we can instead use what is called the amplitude rule. The range is fundamental to this calculation.