What is The Interquartile Range Formula?
The interquartile range, or IQR (also called the midspread or middle fifty), is the difference between the third and the first quartile in a data set. The IQR is a measure of how spread out your data is around the mean. The IQR formula is:
IQR = Q3 – Q1
Where Q3 is the upper quartile and Q1 is the lower quartile.
What is the Interquartile Range Formula Used For?
The IQR formula is a measure of spread, it is primarily used to build box plots. It can also be used as a test for normal distribution and to find outliers in a data set.
IQR as a test for normal distribution
The interquartile range formula can also be used in conjunction with the mean and standard deviation to test whether or not a population has a normal distribution. The formula to determine whether or not a population is normally distributed are:
Q1 – (σ z1) + X
Q3 – (σ z3) + X
Where Q1 is the first quartile, Q3 is the third quartile, σ is the standard deviation, z is the standard score (“z-score“) and X is the mean. In order to tell whether a population is normally distributed, solve both equations and then compare the results. If there is a significant difference between the results and the first or third quartiles, then the population is not normally distributed.
The IQR as a way to determine outliers
The interquartile range formula can be used to find outliers. Outliers are high or low values that fall below Q1-1.5(IQR) or above Q3+1.5(IQR). These outliers will be beyond the whiskers of a boxplot.