Outliers: Effect and the Keep-or-Remove Choice

Lesson 2 of 2: Interpret Data in Context

In this lesson:

• See how an outlier distorts a conclusion
• Decide whether to keep or remove an outlier

Learning Objectives for This Unit

By the end of this unit, you should be able to:

1. Describe shape, center, and spread in context
2. Name the direction of skew correctly
3. Interpret two-group differences in context
4. Explain how an outlier affects each statistic
5. Decide whether to keep or remove an outlier

Should You Take This Job?

A job posting brags: the average employee earns $90,000.

• Sounds great — should you take the job on that number?
• Be suspicious of any "average" without the data's shape

That $90k figure can be true and still mislead. Let's see why.

The Salary Data Behind the Average

• Nine employees earn $40k–$60k (a tight cluster)
• One owner earns $500k (a lone outlier)

Predict the mean and the median before advancing.

Mean Inflated, but Median Stays Honest

For the salary data:

• Mean $90k — dragged up by the owner
• Median $50k — where the nine employees sit

Which describes a typical employee? The median.

The $90k average reflects the owner, not a typical worker.

An Outlier Doesn't Move All Statistics

Recompute all four for the salary data:

• Mean and SD — jump dramatically (non-resistant)
• Median and IQR — barely move (resistant)

"The outlier messes up the data" is too crude — it wrecks only mean and SD.

The Standard Deviation Misleads Too

The owner's $500k also inflates the SD.

• Values now sit far from the inflated mean → SD balloons
• A spread claim based on SD would also mislead

Among the nine workers, salaries are actually quite consistent.

Misleading Versus Honest: Two Conclusions

Same salary data, two stories:

• Misleading (mean): "The average salary is $90,000."
• Honest (median): "A typical employee earns about $50,000."

The outlier's danger is the false story a non-resistant statistic tells.

Your Turn: Correct the Interpretation

Clinic waits: most 10–20 minutes, one emergency at 180 minutes. A report says "average wait is 35 minutes."

Explain why that misleads, then write the corrected interpretation.

Use a resistant statistic, then advance.

Answer: The 180-minute outlier inflated the mean. A typical patient waits about 15 minutes.

So Should You Just Delete It?

An outlier distorts the story — so delete it?

• That instinct is wrong — and avoiding it is the key judgment
• Some outliers are genuine, valuable information

Don't delete first. Investigate first — find out where it came from.

Outliers Are Not Automatically Errors

An outlier is just an unusual value — and unusual values come in two kinds:

• A genuine error (typo, broken sensor)
• A real, rare event that actually happened

You can't tell which without investigating. Erasing a real value falsifies data.

Two Cases, Two Different Calls

• 7-inch adult height → almost certainly a typo → error
• 108° summer day → a real, rare heat wave → keep it

Same flag, opposite decisions — because the source differs.

The Four-Step Outlier Decision Protocol

When you find an outlier:

1. Investigate — where did the value come from?
2. Decide — error or legitimate rare value?
3. Document — record the choice and why
4. Report — state its effect on your conclusion

This replaces impulsive deletion with a defensible, transparent choice.

How to Report a Kept Outlier

If you keep a legitimate outlier, report it carefully:

• Use resistant statistics (median, IQR) for the typical case
• Report the outlier separately as a flagged observation

Typical highs are around 90°, with one record day at 108°.

The typical case stays honest; the rare event stays visible.

Your Turn: Keep or Remove?

Reaction times: mostly 200–400 ms, one entry reads 9000 ms (nine seconds).

Decide keep or investigate, and justify in one sentence.

Name what you'd check. Decide, then advance.

Answer: Investigate — 9000 ms is implausibly long; check whether the subject was distracted or the timer glitched before keeping or removing.

Full Task: Run the Whole Protocol

Given a data set with one outlier in context:

1. Investigate its likely source
2. Decide error or legitimate
3. Document with a justification
4. Report its effect on your conclusion

Do the whole protocol unaided.

Answer: A documented keep-or-remove decision, with resistant statistics and a flag if kept.

Key Takeaways From This Lesson

✓ An outlier hits mean and SD, not median and IQR

✓ The wrong statistic tells a misleading story

✓ Investigate, decide, document, report

Outliers can be errors or real values

Keep a real outlier, but flag it separately

Next: fitting data to a normal model.