# Interquartile Range Calculator

Instructions: This interquartile range calculator will calculate the IQR, showing step-by-step calculations, for a sample data set you specify in the form below:

Name of the variable (Optional) =

The Interquartile Range is a very commonly used measure of dispersion, to assess how spread the data of a distribution are. The same role is fulfilled by the standard deviation , but the interquartile range has a specific characteristic that makes usable for ordinal data, and it is also less sensitive to outliers.

The interquartile range is used also in the box-plot associated to sample data, which often times is used to assess distributional properties of data, same as with a histogram.

One advantage of the interquartile range as a dispersion measurement is that it is more resistant to the presence of outliers, unlike the standard deviation.

## How to Compute the Interquartile Range?

The Interquartile Range is defined as the difference between the first quartile ($$Q_1$$) and third quartile ($$Q_3$$). Mathematically, this is written as:

$IQR = Q_3 - Q_1$

## How to compute the Interquartile in Excel

The easiest way to compute the interquartile range using Excel is by using the formula: "=QUARTILE(data, 3) - QUARTILE(data, 1)", by simply typing it in Excel.

One thing to keep in mind is that there are different conventions to compute quartiles for sample data. Indeed, if you have a sample and try to compute the quartiles with Excel, you will get a different answer than what you get say with Minitab.

The reason for this discrepancy is the why the different statistical software deal with interpolation.

## Interpretation of the interquartile range

As we already mentioned, the interquartile range (IQR) is a measure of dispersion of a distribution. Graphically, it corresponds to the size of the box in a box-plot , which is a graphical device to visualize a distribution and detect outliers .

If instead of computing the interquartile range you need to compute a generic percentile, you can try our percentile calculator , which will show the percentile calculation with all the steps.

Not only visually but outliers can also be detected and found using a formula. The "1.5 times IQR" rule can be also be used as the basis for an outliers calculator, where any point that 1.5 x IQR beyond the first and third quartiles is considered an outlier.