Describe center and spread together
A measure of center does not explain how widely values vary. Mean, median, and mode answer different questions, while range, variance, and standard deviation describe spread. Outliers can affect some measures more than others.
- Use the median when extreme values would distort the mean.
- Use spread to distinguish tightly grouped and widely dispersed data.
- Inspect the distribution before summarizing it with one number.
Interpret relationships cautiously
Correlation measures association, not proof of cause. A relationship can be influenced by a third variable, sampling choices, time trends, or chance. Analytical conclusions should match the design and quality of the evidence.
- Positive correlation means variables tend to move in the same direction.
- Negative correlation means they tend to move in opposite directions.
- A near-zero linear correlation does not eliminate every possible relationship.
Separate signal from analytical error
Outliers may represent errors, unusual but valid events, or important signals. Before removing one, check the source, units, collection process, and business context. Document exclusions so the analysis remains reproducible.
- Confirm whether the value is possible.
- Compare robust and non-robust summaries.
- Explain how inclusion or removal changes the result.
Quick Reference
Important Terms
- Median
- The central observation after values are ordered, or the midpoint of the two central observations for an even count.
- Standard deviation
- A measure of how far observations typically vary from their arithmetic mean.
- Outlier
- An observation that lies unusually far from the broader pattern and requires contextual investigation.
- Correlation
- A numerical description of the direction and strength of association between variables.
- Confidence interval
- A range produced by a method intended to capture an unknown population value at a stated confidence level.
Original Public Practice
Check Your Understanding
1. One value is far higher than every other observation. Which measure of center is generally less affected by it?
Show answer and explanation
Answer: The median.
The median depends on ordered position rather than the magnitude of every observation.
2. A strong association is observed between advertising and sales. What conclusion is justified from correlation alone?
Show answer and explanation
Answer: The variables are associated, but causation has not been established.
Correlation does not rule out confounding variables or alternative explanations.
3. Two datasets have the same mean but very different standard deviations. What does this indicate?
Show answer and explanation
Answer: Their centers are similar, but their values have different amounts of spread.
Standard deviation distinguishes distributions that share a mean but vary differently around it.