# Interquartile range in statistics: What it is and How to find it

Main Index> Basic Statistics> How to find an interquartile range in statistics

A range is a measure of where the first and last data items are in a set; The **interquartile range** is a measure of where the “middle fifty” is in a data set. It’s where the bulk of the values lie, and that’s why it’s preferred over many other measures of spread (i.e. the average or median) when reporting things like school performance on SAT scores.

## Steps:

- Step 1:
**Put the numbers in order.**

**Place parentheses around the numbers above and below the median.**

## What if I Have an Even Set of Numbers?

**Sample question**. Find the IQR for the following data set: 3, 5, 7, 8, 9, 11, 15, 16, 20, 21.

- Step 1:
**Put the numbers in order**.

3, 5, 7, 8, 9, 11, 15, 16, 20, 21.

**Make a mark in the center of the data**:

**Place parentheses around the numbers above and below the mark you made in Step 2 –it makes Q1 and Q3 easier to spot.**

Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data.

**Subtract Q1 from Q3**.

16 – 7 = 9.

*This is your IQR* .

## Find an interquartile range for an **odd** set of numbers: **Alternate Method**

As you may already know, nothing is “set in stone” in statistics: when some statisticians find an interquartile range for a set of odd numbers, they include the median in *both* both quartiles. For example, in the following set of numbers: 1,2,5,6,7,9,12,15,18,19,27 some statisticians

would break it into two halves, including the median (9) in both halves:

(1,2,5,6,7,9),(9,12,15,18,19,27)

This leads to two halves with an even set of numbers, so you can follow the steps above to find the IQR.

## Technology Options

If you’d rather use technology to find the interquartile range, you have plenty of options, including (click for the link):

## What is an Interquartile Range?

### IQR Example

### What is an Interquartile Range Used For?

The IQR is used to measure how spread out the data points in a set are from the mean of the data set. The higher the IQR, the more spread out the data points; in contrast, the smaller the IQR, the more bunched up the data points are around the mean. The IQR range is one of many measurements used to measure how spread out the data points in a data set are. It is best used with other measurements such as the median and total range to build a complete picture of a data set’s tendency to cluster around its mean.

## Where Does the term Interquartile Range Come From?

Who invented the term “Interquartile Range?” In order to find that out, we have to go back to the 19th century.

## History

Macalister’s paper, the Law of the Geometric Mean was actually in response to a question but forward by Francis Galton. However, it wasn’t until 1882 that Galton (“Report of the Anthropometric Committee”) used the upper quartile and lower quartile values and the term “interquartile range” which was defined as twice the probable error. Galton wasn’t just a statistician — he was also an anthropologist, geographer, proto-genetecist and psychometrician who produced more than 340 books. He also coined the statistical terms “correlation” and “regression toward the mean.”

Source: www.statisticshowto.com

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