Range and Inter-quartile range:
Range is defined as the difference between the maximum value and minimum value in a data set. The minimum and maximum values are useful to know, and helpful in identifying outliers, but the range is extremely sensitive to outliers and not very useful as a general measure of dispersion in the data. We know that measures of central tendencies at one point have the issue with the outliers so, to overcome this we can look at the range of the data after dropping values from each end.
Range = Maximum value – Minimum value
A common measurement of variability is Inter-Quartile Range which is the difference between the 25th percentile and the 75th percentile. The data set having more variables has the larger IQR.
The first quartile and the third quartile, and these are often labeled Q1 and Q3, respectively.
It is calculated as difference between Q3 and Q1.
IQR = Q3 – Q1 , where Q1 is 25th percentile and Q3 is 75th percentile.
The IQR is used to plot box plots which are graphical representations of a probability distribution. The length of the box in a box plot is IQR. For a symmetric distribution, the median equals the midline value is nothing but the average of the first and third quartiles, hence half of the IQR equals the median absolute deviation (MAD).
The half of the IQR is termed as quartile deviation or semi-inter quartile range.
In Excel, the formula:
“=QUARTILE(A1:A25, 3)-QUARTILE(A1:A25, 1)”
will calculate the interquartile range and “=MAX(A1:A25)-MIN(A1:A25)” will find the range.
