Range and Interquartile Range

In the most simplest term , range referred as the difference between the maximum and the minimum value .

Example :- For the dataset [23,25,34,27,38]
The maximum value is 38 and the minimum value is 23.
The range wil be  (38 - 23) = 15.
However ,if there will be an outliers in the data , range cannot be considered as the effective measure of the data inspection.

Example :- In the above dataset ,[23,25,34,27,38]
Let us suppose a new value 92.
So ,the new dataset will be like [23,25,34,27,38,92]
The maximum value is 92  and the minimum value is 23.
The range wil be  (92 - 23) = 69.
As ,we can see most of the data lies between the value 23 to 38.


To overcome this issue ,the interquartile range is used and which is the range of the 50 % values in the dataset.
It can be calculated as the difference between the 75th and 25th percentile values.It is the place where majority of data lies.And can provide the central tendency of data.
Let us understand this with an example:-
Assume a dataset having the value as
[1, 3, 4, 5, 5, 6, 7, 11]
so, we will take the range from the value 4,5,5,6.
so , the IQR =6-4 =2.


Further Reading :- https://en.wikipedia.org/wiki/Range_(mathematics)