In statistics, we’re frequently interested in understanding just how “spcheck out out” the values are in a distribution.

You are watching: Is the interquartile range a resistant measure of spread

One renowned method to measure spreview is the interquartile range, which is calculated as the difference between the first quartile and the 3rd quartile in a datacollection. Quartiles are sindicate worths that break-up up a datacollection right into four equal parts.

## Example: Calculating the Interquartile Range

The adhering to instance reflects how to calculate the interquartile variety for a provided dataset:

Step 1: Ararray the worths from smallest to largest.

58, 66, 71, 73, 74, 77, 78, 82, 84, 85, 88, 88, 88, 90, 90, 92, 92, 94, 96, 98

2. Find the median.

58, 66, 71, 73, 74, 77, 78, 82, 84, 85, 88, 88, 88, 90, 90, 92, 92, 94, 96, 98

In this instance, the median is in between 85 and 88.

3. The median splits the dataset into two halves. The median of the lower half is the lower quartile and the median of the top half is the top quartile:

58, 66, 71, 73, 74, 77, 78, 82, 84, 85, 88, 88, 88, 90, 90, 92, 92, 94, 96, 98

4. Calculate the interquartile variety.

In this situation, the first quartile is the average of the middle 2 worths in the lower fifty percent of the data collection (75.5) and also the 3rd quartile is the average of the middle 2 values in the top half of the data collection (91).

Thus, the interquartile array is 91 – 75.5 = 15.5

## The Interquartile Range is Not Affected By Outliers

One factor that civilization like to usage the interquartile array (IQR) as soon as calculating the “spread” of a datacollection is bereason it’s resistant to outliers. Since the IQR is ssuggest the variety of the middle 50% of information values, it’s not impacted by too much outliers.

To demonstrate this, take into consideration the adhering to dataset:

<1, 4, 8, 11, 13, 17, 17, 20>

Here are the miscellaneous steps of spreview for this dataset:

Interquartile range: 11Range: 19Standard deviation: 6.26Variance: 39.23

Now, think about the same dataset but via a severe outlier added to it:

<1, 4, 8, 11, 13, 17, 17, 20, 150>

Here are the assorted measures of spread for this dataset:

Interquartile range: 12.5Range: 149Standard deviation: 43.96Variance: 1,932.84

Notice just how the interquartile range transforms just slightly, from 11 to 12.5. However, every one of the various other actions of dispersion change dramatically.

See more: Some Of The Sample Values Are Negative, But Can The Standard Deviation Ever Be Negative?

This demonstprices that the interquartile array is not impacted by outliers like the various other actions of dispersion. For this factor, it’s a trustworthy way to meacertain the spread of the middle 50% of values in any kind of distribution.