What is the Range Formula?
Range formula refers to the formula which is used in order to calculate the difference between the maximum value and the minimum value of the range and according to the formula the minimum value is subtracted from the maximum value in order to determine the range.
Of the given dataset, which provides statisticians and the mathematician with a better understanding of the data set how varied it is. It is the simplest approach to calculate variance in statistics.
Explanation
It is quite simple and easy to use as the formula states its Maximum value less minimum value of the given sample. Therefore, the variance between Maximum value and the minimum value is the Range and even though that is simple to use and understand it requires to interpret properly.
For example, if there is an outliner in the data the range would get influenced by the same and would get the result will lead to misrepresentation. Take a practical example for given data 2, 4, 7, 7, 100 then the range would be 100 – 2 which is 98 but as one can see that the data range lies below 10 but considering and interpreting that data is within 98 will lead to misrepresentation. Hence the interpretation of Range should be conducted with due consideration.
Examples
Example #1
Consider following given dataset 2,2,4,4, 4, 6,7,7,8, 8, 8, 9 ,9, 9, 9, 9. You are required to calculate the Range for this sample.
Solution:
- Maximum value = 9
- Minimum value = 2
Range = 9 – 2
Range = 7
Example #2
Mr. Stark, a scientist who is working for 10 years with a company called Dream moon. Mr. Arora his supervisor is conducting an experiment on human health and has collected few sample data of male height which are 162, 158, 189, 144, 151, 150, 151, 178, 155, 160, he is perplexed now and wants to know how much data is varied. Mr. Stark who is an experienced statistician has been approached by his supervisor Mr. Arora to remove his confusion as to about variation of the formula. Mr. Arora is required to provide an answer to his supervisor, you are required to calculate how much is the data varied?
Solution:
Range = maximum value – minimum value
- Maximum value = 189
- Minimum value = 144
Range = 189 – 144
Range = 45
The data or the sample collected has a variation of 45.
Example #3
Mr. Buffet a well-known and esteemed investor around the world are now considering US market stock and is in the process of analyzing a few of them where he wants to invest. The list includes major blue-chip companies in the US. Below are the given shortlisted stock or securities along with their latest stock market price which is denoted in US$, where he is considering investing in.
You are required to calculate Range and come up with the variation the list has.
Solution:
Below is given data for calculation of the range.
Using the above information, the calculation of Max Value in excel will be as follows,
Max Value = 204.66
Calculation of Min Value in excel as follows,
Min Value = 45.93
Therefore, calculation of range is as follows,
Range = 204.66 – 45.93
Range will be –
Range = 158.73
Uses of Range Formula
The range in its own way is a very easy and very basic to understand of how the numbers in the given data set or given sample are spread out because as stated earlier it is relatively easy to do the calculation as there is the only required of a very basic arithmetic operation which is just subtracting the minimum from the maximum value, but the range it has few more applications for a given data set or a given sample in statistics. The range is also useful in estimating another measure of spread which is called variance or the standard deviation.
The range as mentioned earlier can only inform about the basic details i.e. where the spread of a given sample or given set of data will lie. By giving the difference or say the variance between the highest and the lowest values of a given sample or given dataset it gives one an information or a rough idea about the significant extreme observations as to how widely spread-out those are, but again it gives no hint or any information as about the other data points that where they would lie, which is the main weakness of using the range equation.
The range as discussed above is useful for depicting the spread within a given sample or a given dataset and further is also used for comparing the resultant spread between the same given sample or same given datasets.
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