š Covariance Calculator
Calculate sample or population covariance between two paired variables.
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Please enter valid values.
Formula and Explanation
Calculate sample or population covariance between two paired variables.
| Concept | Formula or rule |
|---|---|
| Covariance Calculator | Sample covariance = Ī£[(xįµ¢āxĢ)(yįµ¢āČ³)] / (nā1) |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: When larger X values tend to occur with larger Y values, covariance is positive.
ā Positive = move together Ā· Negative = move oppositely
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
ā ļø
Using unpaired observations
Each X must correspond to the Y in the same position.
Each X must correspond to the Y in the same position.
ā ļø
Comparing covariance across units
Covariance magnitude depends on measurement units.
Covariance magnitude depends on measurement units.
ā ļø
Interpreting zero as independence
Zero covariance only means no linear co-movement.
Zero covariance only means no linear co-movement.
Practice Questions
1. If X and Y rise together, what sign is covariance?
Answer: Positive.
2. Is covariance unitless?
Answer: No.
3. What standardizes covariance?
Answer: The correlation coefficient.
Frequently Asked Questions
How is covariance related to correlation?ā¾
Correlation standardizes covariance by both standard deviations.
Can covariance exceed 1?ā¾
Yes. It is not limited to ā1 and 1.
What does negative covariance mean?ā¾
As one variable rises, the other tends to fall.