Outliers and Their Effects

Most datasets contain some variation. Measurements are rarely identical, people differ from one another, and experimental results naturally fluctuate.

Sometimes, however, one value is very different from the rest of the data.

This unusual value may be an outlier.

Consider:

12, 13, 13, 14, 14, 15, 47

Most values are between 12 and 15, but 47 is far away from the others.

That should immediately make us ask:

Why is this value so different?

An outlier may be caused by a mistake—but it may also be completely genuine. Outliers can reveal measurement problems, unusual events, natural variation, or even important new discoveries.

The correct scientific response is therefore not:

"Delete the strange number."

It is:

"Investigate why the number is unusual."

What Is an Outlier?

An outlier is a data value that is unusually far from the other values in a dataset.

For example:

5, 6, 6, 7, 7, 8, 25

The value:

25

appears unusually high compared with the rest of the data.

It may be an outlier.

Now consider:

5, 6, 7, 8, 9, 10, 11

There is no obvious outlier.

The values gradually increase without one value being dramatically separated from the others.

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Outliers Can Be High or Low

An outlier does not have to be unusually large.

Consider:

2, 18, 19, 20, 20, 21, 22

The value:

2

is unusually low.

It may be a low outlier.

Now consider:

18, 19, 20, 20, 21, 22, 61

The value:

61

may be a high outlier.

Both deserve investigation.

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How Can We Recognize an Outlier?

For small datasets, an obvious outlier can sometimes be identified by:

• ordering the data
• looking for unusually large gaps
• constructing a graph
• comparing the value with the overall pattern

Consider:

10, 11, 12, 12, 13, 13, 14, 41

Ordered data make the unusual value easy to see.

There is only a difference of 1 between most neighbouring values.

Then there is a jump from:

14 to 41

This large gap suggests that 41 deserves closer examination.

However, simply "looking unusual" is not always enough to formally classify a value as an outlier. More advanced statistics use specific mathematical rules.

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Visualizing Outliers

Graphs can make outliers much easier to identify.

Imagine these measurements:

21, 22, 22, 23, 24, 23, 22, 51

Most points would form a cluster around:

21–24

One point would appear far away at:

51

This visual separation can immediately draw attention to the unusual observation.

Useful displays for detecting unusual values include:

• dot plots
• scatter plots
• box plots
• histograms
• line graphs in some contexts

Where Do Outliers Come From?

There are many possible causes.

An outlier might result from:

Measurement error

A thermometer was read incorrectly.

Recording error

A student records:

82 cm

instead of:

28 cm

Equipment malfunction

A sensor briefly produces an incorrect reading.

Procedural mistake

One trial was conducted differently from the others.

Uncontrolled variable

Something unexpected changed during one trial.

Natural variation

One organism genuinely differs from the others.

Unusual event

Something rare but real occurred.

Genuine scientific phenomenon

The unusual result reveals something previously unnoticed.

This is why scientists should investigate outliers before deciding what to do with them.

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Outliers Caused by Recording Errors

Suppose plant heights are:

21 cm, 23 cm, 22 cm, 24 cm, 220 cm, 23 cm

The value:

220 cm

looks suspicious.

Checking the laboratory notebook reveals that the original measurement was:

22.0 cm

The decimal point was accidentally omitted.

In this situation, the problem is a recording error.

If the original measurement can be verified, correcting the transcription is justified.

This is very different from deleting a result simply because you do not like it.

---

Outliers Caused by Experimental Problems

Suppose a toy car travels a fixed distance in:

2.41 s

2.38 s

2.43 s

6.81 s

2.40 s

During the fourth trial, the car struck the side of the ramp and nearly stopped.

The unusually high time has an identifiable experimental cause.

A scientist might:

• document what happened
• classify the trial as invalid for the intended procedure
• repeat the trial
• explain any exclusion from the analysis

The important point is that the decision is based on evidence, not on whether the result fits the expected pattern.

Genuine Outliers

Now suppose you measure the heights of plants grown under identical conditions:

18 cm, 19 cm, 20 cm, 21 cm, 20 cm, 34 cm

You check:

• the measurement
• the records
• the equipment
• the procedure

Everything appears correct.

The 34 cm plant may simply be unusually tall.

Perhaps it differs genetically or responded differently to the conditions.

In this case, the outlier may be real data.

Removing it simply because it is unusual could hide important biological variation.

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Outliers Can Lead to Discoveries

Sometimes unusual observations are scientifically interesting precisely because they do not fit expectations.

An unexpected observation might indicate:

• a previously unknown variable
• an unusual organism
• a new physical effect
• a rare event
• an incorrect assumption
• a problem with an existing model
• a new research question

Scientists should therefore be curious about unusual data.

An outlier can sometimes be a problem to solve rather than a problem to remove.

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Outliers and the Mean

Outliers can have a strong effect on the mean because the mean uses every value in the dataset.

Consider:

8, 9, 10, 11, 12

Mean:

(8 + 9 + 10 + 11 + 12) ÷ 5

= 50 ÷ 5

Mean = 10

Now replace 12 with 52:

8, 9, 10, 11, 52

Mean:

(8 + 9 + 10 + 11 + 52) ÷ 5

= 90 ÷ 5

Mean = 18

One extreme value changed the mean from:

10 to 18

Yet four of the five values are still between 8 and 11.

The mean has been pulled toward the outlier.

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High Outliers Pull the Mean Up

Consider:

10, 11, 11, 12, 56

Mean:

100 ÷ 5 = 20

Without the outlier:

10, 11, 11, 12

Mean:

44 ÷ 4 = 11

The high outlier has increased the mean dramatically.

In general:

A very high outlier tends to pull the mean upward.

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Low Outliers Pull the Mean Down

Consider:

−30, 20, 21, 22, 22

Mean:

55 ÷ 5 = 11

Without the unusually low value:

20, 21, 22, 22

Mean:

85 ÷ 4 = 21.25

The low outlier has pulled the mean downward.

In general:

A very low outlier tends to pull the mean downward.

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Why Is the Mean Sensitive to Outliers?

The mean uses the numerical size of every value.

An extreme value changes the total substantially.

Since:

Mean = sum of values ÷ number of values

a large change in the sum changes the mean.

This is why the mean is described as sensitive to outliers.

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Outliers and the Median

The median behaves differently.

Consider:

8, 9, 10, 11, 12

Median = 10

Now:

8, 9, 10, 11, 52

Median = 10

The extreme value changed dramatically, but the median did not change.

This is because the median depends primarily on the position of values, not their exact numerical size.

For this reason, the median is considered more resistant or robust to outliers than the mean.

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Comparing Mean and Median with an Outlier

Consider annual incomes:

$30,000

$32,000

$34,000

$36,000

$368,000

Mean:

$500,000 ÷ 5 = $100,000

Median:

$34,000

The mean of $100,000 is mathematically correct.

But four of the five people earn $36,000 or less.

The median may therefore give a more useful description of the centre of this particular dataset.

Outliers and the Range

Outliers can also have an enormous effect on the range.

Consider:

12, 13, 14, 15, 16

Range:

16 − 12 = 4

Now:

12, 13, 14, 15, 50

Range:

50 − 12 = 38

The range increased from:

4 to 38

This happens because the range depends entirely on the:

minimum and maximum values

If an outlier becomes either the minimum or maximum, it can dramatically change the range.

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Comparing a Dataset With and Without an Outlier

Consider:

Original Dataset

14, 15, 15, 16, 16, 17, 47

Mean:

140 ÷ 7 = 20

Median:

16

Range:

47 − 14 = 33

Now examine the dataset without 47:

Dataset Without the Outlier

14, 15, 15, 16, 16, 17

Mean:

93 ÷ 6 = 15.5

Median:

(15 + 16) ÷ 2 = 15.5

Range:

17 − 14 = 3

Compare:

The outlier strongly affected:

• the mean
• the range

It had relatively little effect on:

• the median

This comparison helps us understand why different statistics respond differently to extreme values.

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Should We Remove the Outlier?

Not automatically.

This is one of the most important rules in data analysis.

An unusual value should not be removed simply because:

• it makes the graph messy
• it changes the mean
• it disagrees with the hypothesis
• it makes the conclusion less convincing
• the researcher does not like it

Removing inconvenient evidence without justification can seriously distort scientific conclusions.

Instead:

Investigate first.

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Questions to Ask About an Outlier

When you identify a possible outlier, ask:

Was the value recorded correctly?

Check the original notes.

Was the measurement made correctly?

Check the method and equipment.

Did something unusual happen during that trial?

Look for procedural problems.

Were the experimental conditions different?

Check the control variables.

Can the measurement be repeated?

Collect additional evidence when appropriate.

Is the unusual value scientifically plausible?

Consider whether it could genuinely occur.

Do similar unusual values appear in other data?

Compare with additional trials or sources.

Only then should you decide how the value should be treated.

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When Excluding an Outlier May Be Justified

Suppose a reaction normally takes approximately 30 seconds.

Recorded times are:

30.2 s

29.8 s

30.4 s

84.7 s

30.1 s

Your laboratory notes state:

"Trial 4: stopwatch not stopped when reaction finished."

There is documented evidence that Trial 4 does not represent the intended measurement.

Excluding it from a calculation may therefore be scientifically justified.

However, the exclusion should be reported and explained.

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When Excluding an Outlier Is Not Justified

Suppose the same values occur:

30.2 s

29.8 s

30.4 s

84.7 s

30.1 s

But there is no known problem with Trial 4.

You should not simply say:

"84.7 doesn't fit, so I deleted it."

Instead, you might:

• check the records
• inspect the equipment
• repeat the measurement
• collect more trials
• report calculations with and without the possible outlier
• discuss its effect on the conclusion

The unusual value itself may contain useful information.

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Compare Results With and Without the Outlier

One useful analytical technique is to calculate statistics both with and without a suspected outlier.

Suppose:

5, 6, 6, 7, 7, 8, 31

With the outlier:

Mean = 70 ÷ 7

Mean = 10

Without 31:

Mean = 39 ÷ 6

Mean = 6.5

That is a large difference.

You can report:

"Including the unusual value gives a mean of 10, while excluding it gives a mean of 6.5."

This makes the impact of the outlier transparent.

It does not secretly hide data from the reader.

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Outliers Can Change Conclusions

Imagine comparing two experimental groups.

Treatment A

10, 11, 11, 12, 12

Mean = 11.2

Treatment B

10, 11, 11, 12, 51

Mean = 19

Looking only at the means could make Treatment B appear dramatically different.

But four of its five measurements are nearly identical to Treatment A.

The difference is largely caused by one unusual value.

Before claiming that Treatment B generally produces higher results, the researcher should investigate the outlier.

This illustrates why data interpretation should never rely blindly on a single statistic.

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Outliers in Scientific Experiments

Suppose students measure the period of a pendulum:

1.42 s

1.39 s

1.41 s

1.98 s

1.40 s

The 1.98 s result should attract attention.

Possible explanations include:

• timing error
• incorrect oscillation count
• different release angle
• changed pendulum length
• recording error

The next scientific step is not automatically deletion.

It is investigation.

Outliers in Biological Data

Biological systems naturally vary.

Suppose plant heights are:

14, 15, 15, 16, 17, 29 cm

The 29 cm plant may appear unusual.

But organisms differ because of factors such as:

• genetics
• development
• environmental conditions
• disease
• access to resources

The plant should not automatically be excluded.

It may represent genuine biological variation.

This is one reason larger sample sizes are especially useful in biology.

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Outliers in Real-World Data

Outliers occur in many areas.

Weather

An unusually hot day may be a genuine extreme weather event.

Sports

A player may have one exceptionally high-scoring game.

Finance

One unusually large transaction can strongly affect average spending.

Housing

One extremely expensive property can increase the mean house price.

Manufacturing

One unusually sized component may indicate a production problem.

Medicine and biology

An unusual measurement might indicate natural variation, an unusual condition, or a measurement problem.

The correct interpretation always depends on context.

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Outliers in Manufacturing

Suppose a factory produces components that should be approximately 50.0 mm long.

Measurements:

49.9, 50.0, 50.1, 49.9, 54.8 mm

The value:

54.8 mm

is worth investigating.

It might indicate:

• a machine malfunction
• incorrect calibration
• damaged equipment
• incorrect measurement
• a genuine defective product

Here, identifying an outlier could help discover a real production problem.

Outliers and Sample Size

Outliers can have a particularly large influence in small datasets.

Consider a dataset with three values:

10, 11, 40

Mean:

61 ÷ 3 ≈ 20.3

The outlier has a major effect.

Now imagine a dataset containing 1,000 observations clustered around 10–12 plus one observation of 40.

That single value will have much less influence on the overall mean.

This is another reason sample size matters when interpreting statistics.

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One Outlier May Not Be an Outlier in a Larger Dataset

Suppose you measure only five values:

10, 11, 12, 13, 25

The value 25 appears isolated.

But after collecting much more data, you obtain:

10, 11, 12, 13, 14, 15, 16, 18, 20, 22, 25

Now 25 may appear less unusual.

Whether a value should be considered an outlier depends partly on the distribution and context of the full dataset.

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Formal Methods for Identifying Outliers

In larger or more advanced datasets, scientists do not always identify outliers simply by looking at the numbers.

Statistical methods can be used.

One common method uses the interquartile range (IQR).

The IQR describes the spread of the middle 50% of the data.

A commonly used rule identifies potential outliers as values:

below Q₁ − 1.5 × IQR

or

above Q₃ + 1.5 × IQR

where:

Q₁ = lower quartile

Q₃ = upper quartile

IQR = Q₃ − Q₁

You do not need this calculation for every simple dataset, but it demonstrates an important idea:

Scientists can use defined statistical criteria rather than personal opinion to identify potential outliers.

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Box Plots and Outliers

A box plot is especially useful for displaying:

• median
• quartiles
• spread
• possible outliers

Potential outliers may appear as individual points beyond the main whiskers of the plot, depending on the convention being used.

This makes box plots useful when comparing the distributions of several datasets.

Outlier Does Not Mean Error

This distinction is essential:

Outlier ≠ mistake

An outlier means:

unusually different observation

It does not automatically mean:

incorrect observation

Similarly:

unusual ≠ impossible

A scientist must investigate before deciding whether the value resulted from error or represents a genuine event.

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Anomaly and Outlier

The words outlier and anomalous result are often used in similar ways in school science.

An anomalous result is one that does not fit the expected or general pattern.

An outlier is a value unusually separated from the rest of a dataset.

In many simple investigations, the same value may be described as both.

However, the terms emphasize slightly different ideas:

Outlier → statistical position in the dataset

Anomaly → unexpected relationship or pattern

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Outliers and Scientific Integrity

Imagine a student predicts that increasing temperature will increase reaction rate.

Four results support the prediction.

One does not.

The student deletes the unwanted result and reports only the four supportive values.

This is poor scientific practice.

Scientific integrity requires researchers to:

• report data honestly
• investigate unusual results
• explain exclusions
• acknowledge uncertainty
• avoid changing evidence to fit expectations

A conclusion should follow the evidence.

The evidence should never be altered simply to produce the desired conclusion.

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Reporting Outliers

A strong scientific report might say:

"Trial 4 produced a reaction time of 84.7 s, substantially higher than the other trials (29.8–30.4 s). Laboratory notes show that the stopwatch was not stopped when the reaction ended. The trial was therefore excluded from the calculated mean and repeated."

This clearly explains:

• the unusual value
• why it was unusual
• what caused the problem
• why it was excluded
• what was done next

That is much stronger than:

"I removed 84.7 because it was an outlier."

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Worked Example: With and Without an Outlier

A student measures plant growth:

8, 9, 9, 10, 10, 11, 34 cm

With the Outlier

Sum:

8 + 9 + 9 + 10 + 10 + 11 + 34 = 91

Mean:

91 ÷ 7 = 13 cm

Median:

10 cm

Range:

34 − 8 = 26 cm

Without 34

Dataset:

8, 9, 9, 10, 10, 11

Sum = 57

Mean:

57 ÷ 6 = 9.5 cm

Median:

(9 + 10) ÷ 2 = 9.5 cm

Range:

11 − 8 = 3 cm

The suspected outlier changes:

Mean: 9.5 → 13

Range: 3 → 26

Median: 9.5 → 10

This shows why outliers can dramatically influence some statistics while having much less effect on others.

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Worked Example: Evaluating the Cause

Reaction times:

42 s, 41 s, 43 s, 40 s, 91 s

The value 91 s appears unusual.

Step 1: Check the record

Was 91 copied correctly?

Step 2: Check the procedure

Was the trial performed in the same way?

Step 3: Check equipment

Was the timer functioning correctly?

Step 4: Check conditions

Did temperature, concentration, or another variable change?

Step 5: Repeat if possible

Does another trial produce a similar result?

Step 6: Decide and document

Retain or exclude the value based on evidence and explain the decision.

This is much more scientific than simply removing the largest number.

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Common Mistakes

Assuming the largest value is always an outlier

A maximum is not automatically an outlier.

Assuming outliers must be high

Outliers can be unusually high or unusually low.

Deleting every unusual value

Outliers should be investigated first.

Removing data because they disagree with the hypothesis

This introduces bias and violates scientific integrity.

Assuming an outlier is definitely an error

It may represent genuine variation or an important phenomenon.

Ignoring outliers completely

Outliers can dramatically affect statistical calculations and conclusions.

Looking only at the mean

Compare mean, median, range, graphs, and the original values.

Forgetting that the range is sensitive to outliers

An extreme minimum or maximum can dramatically increase the range.

Assuming the median is unaffected by every possible outlier

The median is less sensitive, not magically immune to all changes in a dataset.

Correcting data without evidence

Only correct a value if there is evidence that a recording or transcription error occurred.

Hiding excluded results

Scientific reports should explain important exclusions.

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Key Terms

Outlier — A data value unusually far from most other observations.

Anomalous result — A result that does not fit the general or expected pattern.

Extreme value — An unusually high or low observation.

Dataset — A collection of related data values.

Distribution — The way values are arranged and spread throughout a dataset.

Cluster — A group of data values located relatively close together.

Gap — A region between observations containing few or no values.

Mean — The sum of all values divided by the number of values.

Median — The middle value of an ordered dataset.

Range — The difference between the maximum and minimum values.

Variability — The amount of difference or spread among observations.

Robust/Resistant statistic — A statistic that is relatively unaffected by extreme observations.

Measurement error — Difference introduced during the process of measuring.

Recording error — A mistake made when writing, entering, or transferring data.

Experimental error — Variation or problems associated with experimental measurements or procedures.

Natural variation — Genuine differences that occur naturally within a system or population.

Systematic error — An error that consistently shifts measurements in a particular direction.

Random error — Unpredictable variation between measurements.

Sample size — The number of observations in a dataset or sample.

Quartile — A value used to divide ordered data into four sections.

Interquartile range (IQR) — The difference between the upper and lower quartiles, representing the spread of the middle 50% of data.

Box plot — A graphical display showing features of a distribution such as median, quartiles, spread, and potential outliers.

Data exclusion — The removal of a measurement from a particular analysis according to a justified rule or reason.

Scientific integrity — Honest and responsible collection, analysis, and reporting of scientific evidence.

Bias — A systematic influence that can distort evidence or its interpretation.

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Key Takeaways

• An outlier is a value unusually different from most of the other observations.
• Outliers can be unusually high or unusually low.
• Ordering data and graphing them can help reveal possible outliers.
• Large gaps between observations may indicate an unusual value.
• Outliers can result from measurement errors, recording errors, equipment problems, procedural mistakes, natural variation, or genuine unusual events.
• An outlier is not automatically an error.
• Unexpected results can sometimes lead to important scientific discoveries.
• The mean is sensitive to outliers because every numerical value contributes to it.
• High outliers tend to pull the mean upward.
• Low outliers tend to pull the mean downward.
• The median is generally more resistant to extreme values than the mean.
• The range is highly sensitive to outliers because it depends on the minimum and maximum values.
• Comparing statistics with and without an outlier can reveal how strongly it influences the dataset.
• Outliers can substantially change the apparent differences between groups.
• Never delete an observation simply because it does not support your hypothesis.
• Investigate unusual values before deciding how they should be treated.
• Check records, equipment, procedures, and experimental conditions.
• Repeat measurements when appropriate and possible.
• An outlier may be excluded when there is a clear scientific or methodological justification.
• Any important exclusion should be documented and explained.
• Larger sample sizes can reduce the influence of a single unusual observation on some statistics.
• Formal methods such as the IQR rule can help identify potential outliers objectively.
• Box plots are useful for visualizing distributions and potential outliers.
• Outliers and anomalies are related concepts but are not always exactly the same.
• Scientific integrity requires researchers to report and evaluate unexpected evidence honestly.
• Good data analysis asks why an unusual result occurred rather than simply trying to make it disappear.

When you encounter an unusual result, ask:

Is the value genuinely unusual?

Was it recorded correctly?

Was it measured correctly?

Did something unusual happen during the trial?

Could it represent real variation?

Can I collect more evidence?

How much does it affect the mean, median, and range?

Would my conclusion change depending on whether it is included?

And most importantly:

Do I have a scientific reason for treating this value differently from the others?

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Check Your Understanding

1. Identify the likely outlier:

12, 13, 14, 13, 15, 14, 46

2. Identify the likely outlier:

−25, 8, 9, 10, 11, 12

3. Explain why the largest value in a dataset is not automatically an outlier.

4. Calculate the mean:

8, 9, 10, 11, 12

Then calculate the mean after replacing 12 with 52.

How did the outlier affect the mean?

5. Find the median of both datasets in Question 4. How did the outlier affect the median?

6. Calculate the range of both datasets in Question 4. How did the outlier affect the range?

7. Why is the mean more sensitive to extreme values than the median?

8. A student records:

2.31 s, 2.29 s, 2.33 s, 7.81 s, 2.30 s

What should the student do before deciding whether to exclude 7.81 s?

9. During the unusual trial in Question 8, the student recorded that the car crashed into another object. Explain what the student should do next.

10. A plant in an experiment grows much taller than all the other plants, but there is no evidence of measurement or procedural error. Should the plant automatically be removed from the dataset? Explain.

11. Explain the difference between an outlier and a recording error.

12. Give three possible causes of an outlier in a scientific investigation.

13. Explain how an outlier can affect the range.

14. Why might an outlier have a greater effect on the mean of a small dataset than on the mean of a very large dataset?

15. A factory measures:

49.9, 50.0, 50.1, 50.0, 56.8 mm

Why should the 56.8 mm component be investigated?

16. Explain why deleting results that disagree with your hypothesis is poor scientific practice.

17. A dataset is:

15, 16, 16, 17, 18, 74

Calculate the mean, median, and range.

Then calculate them again without 74.

18. Which of the mean, median, and range in Question 17 was affected most strongly by the outlier? Explain.

19. Why might scientists report an analysis both with and without a suspected outlier?

20. Challenge: A scientist obtains:

20.1, 20.3, 20.2, 20.4, 31.8, 20.2

The scientist cannot find any obvious measurement, recording, or equipment error.

Explain how the scientist should investigate the 31.8 result, what additional evidence could be collected, and why simply deleting the value would not be scientifically justified.