*50*

An **outlier** is a data point that lies abnormally far away from other values in a dataset.

We often define a data point to be an outlier if it is 1.5 times the interquartile range greater than the third quartile or 1.5 times the interquartile range less than the first quartile of a dataset.

**Note**: The interquartile range is the difference between the third quartile (75th percentile) and the first quartile (25th percentile) in a dataset.

The following scenarios share examples of outliers in real life situations.

**Example 1: Outliers in Income**

One real-world scenario where outliers often appear is income distribution.

For example, the 25th percentile (Q1) of annual income in a certain country may be $15,000 per year and the 75th percentile (Q3) may be $120,000 per year.

The interquartile range (IQR) would be calculated as $120,000 â€“ $15,000 = $105,000.

This means that anyone with an income outside of the following boundaries would be considered an outlier:

**Lower Boundary**: Q1 â€“ 1.5*IQR = $15,000 â€“ 1.5*$105,000 = -$142,500**Upper Boundary**: Q3 + 1.5*IQR = $120,000 + 1.5*$105,000 = $277,500

Someone like Elon Musk who has a net worth in the billions of dollars would be considered an outlier in terms of annual income.

**Note**: The value for outliers beyond the lower boundary will not always make sense, e.g. itâ€™s not possible to earn a negative annual income.

**Example 2: Outliers in Breath-Holding**

Another real-world scenario where outliers often appear is breath-holding.

For example, the 25th percentile (Q1) for how long individuals can hold their breath is around 15 seconds while the 75th percentile (Q3) is around 75 seconds.

The interquartile range (IQR) would be calculated as 75 â€“ 15 = 60.

This means that anyone who is able to hold their breath outside of the following boundaries would be considered an outlier:

**Lower Boundary**: Q1 â€“ 1.5*IQR = 15 â€“ 1.5*60 = -75 seconds**Upper Boundary**: Q3 + 1.5*IQR = 75 + 1.5*60 = 165 seconds

Any freedivers who can hold their breath for 10 minutes or longer would be considered outliers because they can hold their breath much longer than 165 seconds.

**Example 3: Outliers in Animal Height**

Another real-world scenario where outliers often appear is height of animals.

For example, the 25th percentile (Q1) of horse height is around 5 feet and the 75th percentile (Q3) is around 5.5 feet.

The interquartile range (IQR) would be calculated as 5.5 â€“ 5 = 0.5 feet.

This means that any horse with a height outside of the following boundaries would be considered an outlier:

**Lower Boundary**: Q1 â€“ 1.5*IQR = 5 â€“ 1.5*0.5 = 4.25 feet**Upper Boundary**: Q3 + 1.5*IQR = 5 + 1.5*0.5 = 5.75 feet

According to the Guinness World Records, the record for tallest horse ever is just above 7 feet. Since this is above the upper boundary of 5.75 feet, this horse would clearly be considered an outlier.

**Example 4: Outliers in Movie Ticket Sales**

Another real-world scenario where outliers often appear is movie ticket sales.

For example, the 25th percentile (Q1) of gross ticket sales for movies is around $2 million and the 75th percentile (Q3) is around $15 million.

The interquartile range (IQR) would be calculated as $15 million â€“ $2 million= $13 million.

This means that any movie with gross sales outside of the following boundaries would be considered an outlier:

**Lower Boundary**: Q1 â€“ 1.5*IQR = $2 million â€“ 1.5*$13 million = -$17.5 million**Upper Boundary**: Q3 + 1.5*IQR = $15 million + 1.5*$13 million = $34.5 million

Most Star Wars movies have grossed far more than $34.5 million, which makes them outliers in terms of ticket sales.

**Example 5: Outliers in Points Scored per Game**

Yet another real-world field where outliers often appear is professional sports.

For example, the 25th percentile (Q1) of points scored by NBA players is around 5 points per game and the 75th percentile (Q3) is around 15 points per game.

The interquartile range (IQR) would be calculated as 15 â€“ 5 = 10 points.

This means that any player who averages outside of the following boundaries would be considered an outlier:

**Lower Boundary**: Q1 â€“ 1.5*IQR = 5 â€“ 1.5*10 = -10 points**Upper Boundary**: Q3 + 1.5*IQR = 15 + 1.5*10 = 30 points

During many NBA seasons, the highest scoring player typically averages just over 30 points per game which makes them an outlier.

**Additional Resources**

The following tutorials explain how to find outliers in datasets using various statistical software:

How to Find Outliers in Excel

How to Find Outliers in R

How to Find Outliers in Python

How to Find Outliers in SPSS