# Interquartile Range Formula: What is it?

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## 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.

You can calculate the IQR using our online interquartile range calculator. The calculator also works as a quartile calculator.

Need to calculate the interquartile range formula by hand? Check out this video:

### 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.

Frequency chart with boxplot at the top. The outliers are shown as dots outside the range of the whiskers.

Interquartile Range Formula: What is it? was last modified: October 5th, 2015 by

# 7 thoughts on “Interquartile Range Formula: What is it?”

1. Andale Post author

Christian,

It’s just for figuring out if you have outliers.

there’s no need to use it in the interquartile range formula itself.

Stephanie