Comprehensive Calculator Guide
This calculator works out the covariance of two variables for a sample or population, how much they move together, with both means and the correlation for comparison. Study hours and marks for six students have a sample covariance of 35.2, positive because both rise together.
Covariance
It averages the products of paired deviations; sample divides by n − 1, population by N. Its size depends on units, so divide by both SDs to get the correlation; finance uses covariance directly for portfolio risk.
How to Use
- Enter the first variable.
- Enter the second in the same order and choose sample or population.
- Press “Calculate” to see the covariance, means and correlation.
Formula Used
s_xy = Σ(x − x̄)(y − ȳ) ÷ (n − 1)
Practical Examples
- Example 1
- Study and marks: 35.2.
- Example 2
- Heat and coffee: −237.5.
Important Tips
- Sign for direction, r for strength.
- Align the pairs.
- Population for complete data.
Common Mistakes to Avoid
- Reading a big covariance as strong.
- Comparing across units.
- Mixing n and n − 1.
Frequently Asked Questions
- What is covariance?
- How two variables move together.
- Vs correlation?
- Correlation is standardised.
- Negative?
- One falls as the other rises.