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Sample Covariance — result sheet
Calculate the sample covariance of two equal-length paired data sets.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Sample covariance = sum((xi - xbar)(yi - ybar)) / (n - 1).
Covariance describes whether paired observations tend to be above or below their means together. Its magnitude depends on the units of both variables, so correlation is often used when a unit-free measure is needed.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X values — Enter 2-1,000 numbers separated by commas or spaces.
- Y values — Enter the same number of paired values.
Worked example
| Input | Value |
|---|---|
| X values | 1, 2, 3 |
| Y values | 2, 4, 7 |
Sample covariance is 2.5.
Assumptions and limits
- The two lists contain the same number of paired finite observations.
- The sample denominator n-1 is used.
- Covariance describes association in the data and does not establish causation.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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