What is the interquartile range a measure of and how do you work it out?

The interquartile range is a measure of the "spread" of the data and represents the central 50%. It gives us an idea of the degree of variability. A small IQR would suggest the central data are close together and therefore are more consistent, whereas a large IQR would suggest a larger spread of data and therefore more variability. An IQR can be calculated using the following steps:

1) Put the data in numerical order from smallest to largest.

2) The lower quartile (Q1) is calculated using the formula: (n+1)/4 where n is the amount of numbers in the data set.

3) The upper quartile (Q3) is calculated using the formula: 3(n+1)/4

4) The interquartile range (IQR) = Q3-Q1

The IQRs from different datasets can be visually compared from box and whiskers diagrams.

Interquartile range shows how 50% of the data is spread out and measures the reliability or consistency of the given data . It is the difference between the Lower Quartile and the Upper Quartile. The Lower the value of Interquartile range the more reliable and consistent the results are.

Lower Quartile is the position of a quarter of the data and the upper quartile is the position of three quarters of the data when put in order of size.

It is a measure of spread and not to be confused with a measure of central tendency (I.e average). IQR = UQ - LQ