How to Identify an Outlier

How to identify an outlier, step by step: the rule in plain language, solved examples worked one line at a time, and practice questions so you can try it yourself before moving on.

An outlier is a data value that is significantly higher or lower than the rest of the data set. Outliers can result from measurement errors, unusual events, or genuinely extreme observations. On the GED Math test you may need to identify outliers, explain their effect on the mean, or determine which values fall outside the normal range using the IQR (Interquartile Range) fence method.

What Is an Outlier?

Informally, an outlier “doesn’t fit” with the rest of the data. Formally, the most common rule is:

• A value is an outlier if it is more than \(\color{blue}{1.5 \times \text{ IQR }}\) above Q3 or more than \(\color{blue}{1.5 \times \text{ IQR }}\) below Q1.

How to Identify an Outlier Using the IQR Method

Step 1: Find Q1, Q3, and IQR

• Sort the data from least to greatest.
• Q1 = median of the lower half of the data
• Q3 = median of the upper half of the data
• IQR = \(\color{blue}{Q3 – Q1}\)

Step 2: Calculate the fences

• Lower fence = \(\color{blue}{Q1 – 1.5 \times \text{ IQR }}\)
• Upper fence = \(\color{blue}{Q3 + 1.5 \times \text{ IQR }}\)

Step 3: Identify outliers

Any data value below the lower fence or above the upper fence is an outlier.

Step-by-Step Summary

1. Sort the data set.
2. Find Q1 (median of lower half) and Q3 (median of upper half).
3. Calculate \(\color{blue}{\text{ IQR } = Q3 – Q1}\).
4. Lower \(\color{blue}{\text{ fence } = Q1 – 1.5 \times \text{ IQR }}\); Upper \(\color{blue}{\text{ fence } = Q3 + 1.5 \times \text{ IQR }}\).
5. Any value outside these fences is an outlier.

Watch: How to Determine if a Set of Numbers Has Outliers (Video Lesson)

This video demonstrates the full IQR fence method with step-by-step calculations:

Worked Examples

Example 1: Identify any outliers in: 3, 7, 8, 9, 10, 11, 12, 50.

Sorted: 3, 7, 8, 9, 10, 11, 12, 50
Lower half: 3, 7, 8, 9 → \(\color{blue}{Q1 = \frac{(7+8)}{2} = 7.5}\)
Upper half: 10, 11, 12, 50 → \(\color{blue}{Q3 = \frac{(11+12)}{2} = 11.5}\)
\(\color{blue}{\text{ IQR } = 11.5 – 7.5 = 4}\)
Lower \(\color{blue}{\text{ fence } = 7.5 – 1.5(4) = 7.5 – 6 = 1.5}\)
Upper \(\color{blue}{\text{ fence } = 11.5 + 1.5(4) = 11.5 + 6 = 17.5}\)
50 > 17.5 → 50 is an outlier; 3 > 1.5, so 3 is not an outlier.

Example 2: Does the data set 10, 12, 13, 14, 15, 16, 17, 100 contain an outlier?

\(\color{blue}{Q1 = \frac{(12+13)}{2} = 12.5}\); \(\color{blue}{Q3 = \frac{(15+16)}{2} = 15.5}\); \(\color{blue}{\text{ IQR } = 3}\)
Upper \(\color{blue}{\text{ fence } = 15.5 + 4.5 = 20}\)
100 > 20 → 100 is an outlier

Example 3: How does an outlier affect the mean?

Data: 5, 6, 7, 8, 9 → \(\color{blue}{\text{ Mean } = \frac{35}{5} = 7}\)
Replace 9 with 90: 5, 6, 7, 8, 90 → \(\color{blue}{\text{ Mean } = \frac{116}{5} = 23.2}\)
The outlier (90) raised the mean from 7 to 23.2, far from the typical value.

Example 4: Find the outlier: 2, 4, 5, 6, 7, 8, 9, 1.

Sorted: 1, 2, 4, 5, 6, 7, 8, 9
\(\color{blue}{Q1 = \frac{(2+4)}{2} = 3}\); \(\color{blue}{Q3 = \frac{(7+8)}{2} = 7.5}\); \(\color{blue}{\text{ IQR } = 4.5}\)
Lower \(\color{blue}{\text{ fence } = 3 – 6.75}\) = −3.75; Upper \(\color{blue}{\text{ fence } = 7.5 + 6.75 = 14.25}\)
All values are \(\color{blue}{\text{ between } -3.75}\) and 14.25 → No outliers

More Practice: How to Find Outliers (Video)

My Secret Math Tutor explains the outlier identification process with clear examples:

Exercises

1. Find Q1, Q3, IQR, and both fences for: 5, 10, 11, 12, 13, 14, 15, 60.
2. Is 2 an outlier in the set: 2, 20, 22, 24, 25, 28, 30?
3. A student scored 45, 88, 92, 90, 87, 91, 89. Is 45 an outlier?
4. Data: 3, 5, 6, 7, 8, 9, 10. Are there any outliers?
5. Which measure — mean or median — is more affected by an outlier? Explain.

Answers

1. \(\color{blue}{Q1=\frac{(10+11)}{2}=10.5}\); \(\color{blue}{Q3=\frac{(13+14)}{2}=13.5}\); \(\color{blue}{\text{ IQR }=3}\); Lower \(\color{blue}{\text{ fence }=10.5-4.5=6}\); Upper \(\color{blue}{\text{ fence }=13.5+4.5=18}\). Values 5 and 60 are outside the fences: 5 and 60 are outliers
2. Sorted: 2,20,22,24,25,28,30; \(\color{blue}{Q1=20}\); \(\color{blue}{Q3=28}\); \(\color{blue}{\text{ IQR }=8}\); Lower \(\color{blue}{\text{ fence }=20-12=8}\). Since 2 < 8: yes, 2 is an outlier
3. Sorted: 45,87,88,89,90,91,92; \(\color{blue}{Q1=87.5}\); \(\color{blue}{Q3=90.5}\); \(\color{blue}{\text{ IQR }=3}\); Lower \(\color{blue}{\text{ fence }=87.5-4.5=83}\). Since 45 < 83: yes, 45 is an outlier
4. \(\color{blue}{Q1=5}\); \(\color{blue}{Q3=9}\); \(\color{blue}{\text{ IQR }=4}\); Lower fence=−1; Upper \(\color{blue}{\text{ fence }=15}\). All values in range: no outliers
5. The mean is more affected because it includes every value in its calculation. The median only depends on the middle value(s).

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Frequently Asked Questions

What is an outlier and how do you identify it?

An outlier is a value that sits far from the rest of a data set. A quick first step is to sort the data and look for a big gap between a value and its neighbors. In the quiz scores 30, 72, 75, 78, 80, 81, 83, the 30 sits more than 40 points below the next score. To confirm it formally, use the 1.5 × IQR rule.

What is considered an outlier?

The most common rule says a value is an outlier if it is below Q1 − 1.5 × IQR or above Q3 + 1.5 × IQR, where IQR = Q3 − Q1. For example, if Q1 = 20 and Q3 = 30, the IQR is 10 and the fences are 20 − 15 = 5 and 30 + 15 = 45. Any value under 5 or over 45 counts as an outlier.

How do you identify an outlier using the IQR method?

Sort the data, find Q1 and Q3, subtract to get the IQR, then build the fences. For 2, 4, 5, 6, 7, 8, 9, 25, the lower half 2, 4, 5, 6 gives Q1 = 4.5, and the upper half 7, 8, 9, 25 gives Q3 = 8.5. IQR = 4, so the fences are 4.5 − 6 = −1.5 and 8.5 + 6 = 14.5. Since 25 > 14.5, it is an outlier.

How do you identify an outlier in a box plot?

Many box plots mark outliers as separate dots or stars beyond the whiskers, so any point drawn on its own is an outlier. If the plot shows no separate points, read Q1 and Q3 from the edges of the box, compute the IQR, and check whether either whisker end, the minimum or maximum, lies more than 1.5 × IQR beyond the box.

How do you identify an outlier in a scatter plot?

Look for a point that sits far away from the overall pattern of the others. If most points follow a rising trend, such as study hours versus test scores, a student who studied 10 hours but scored 40 would stand out well below the trend. Scatter plot outliers are usually judged by eye, since there is no single fence rule like the IQR for paired data.

What is the effect of removing an outlier?

Removing an outlier changes the mean the most, the median only a little, and often shrinks the range a lot. With 30, 72, 75, 78, 80, 81, 83, the mean is 499 ÷ 7 ≈ 71.3 and the median is 78. Drop the 30, and the mean becomes 469 ÷ 6 ≈ 78.2, while the median moves only to 79. The range shrinks from 53 to 11.

Related Topics

• Finding Range, Quartile, and Interquartile Range
• Mean, Median, Mode, and Range
• Distributions in Line Plot
• Line Plot
• How to Solve the Frequency Distribution Table