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4 Tutorials that teach Range and Interquartile Range (IQR)
Common Core: S.ID.2

# Range and Interquartile Range (IQR)

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Author: Sophia Tutorial
##### Description:

This lesson will explain range and interquartile range (IQR)

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Tutorial

This tutorial will cover the range and the interquartile range. You’ll learn about:

1. Range
2. Interquartile Range

## 1. Range

Range and interquartile range are similar ideas in that they're both actually measured by subtraction, so they're not particularly difficult to calculate.

• Range
• The difference between the largest and smallest number in a data set.
• Interquartile Range
• The difference between the third and first quartiles. It represents the range in which the middle 50% of the data points lie.

While they are calculated similarly, they do measure different measures of variation.

This chart shows the height of the Chicago Bulls basketball team for a particular year:

It's easy to see from the list that the minimum value is 71 and the maximum value is 84.

The range is actually the easiest measure of spread or variation to find: take the maximum value (in this case, the tallest person) and subtract the minimum value (in this case, the shortest person). 84-71=13 inches. This means that every individual on the team falls within a 13 inch range.

• Range

## 2. Interquartile Range

The interquartile range is another measure of spread, but it's median based. To review, the median is the middle number of an ordered data set. Finding the median takes a few steps:

1. First, order the data set (largest to smallest) and then work your way in towards the center until you find the median.
2. Once you have two data sets, a small half and a high half, you can find the middle number of each of those haves.
3. Those three numbers called quartiles.

The three numbers are called:

1. Q1, first quartile: one fourth of the data falls at or below the first quartile
2. The median, which is the second quartile: half the data falls at or below the median
3. and Q3, the third quartile: 3/4 of the data falls at or below the third quartile

The interquartile range, also abbreviated IQR, is the difference between the two quartiles.

• Interquartile Range

This means that half, the middle half, of the data set falls within a 7 inch range, whereas the entire data set falls within a 13 inch range.

Visually, the IQR is the box on a box plot.

The range gives the entire spread of the data set lowest to highest whereas the IQR gives the range of the middle 50%.

The advantage of using IQR over range is if there are outliers, which would disproportionately affect the range, the IQR will not be affected by them.

The range is not the most useful measure of variation but it is the easiest to calculate. The interquartile range is more useful and measures the range of the middle 50%, the most typical middle 50% of the data. It's a useful measure of spread for distributions with outliers or skewness. In fact, you should use IQR as your measure of variation when there are outliers or skewness.

Because the IQR is based on finding the median, it should only be used as the measure of spread when the median is the measure of center. You shouldn't mix and match saying the mean is the measure of center and then reporting IQR as the measure of spread.

Thank you and good luck!

Source: THIS WORK IS ADAPTED FROM SOPHIA AUTHOR JONATHAN OSTERS

Terms to Know
Interquartile Range

The difference between the third and first quartiles. It represents the range in which the middle 50% of the data points lie.

Range

The difference between the largest and smallest number in a data set.

Formulas to Know
Interquartile Range

Range