Covariance
Topic: Economic Data: Census, NSS, Surveys and Statistical Tools · NCERT: Class 11, Ch 6 "Correlation"
Meaning
Covariance measures how two variables vary together. It is the mean of the products of the deviations of X and Y from their own means. A deviation is the gap between a value and the mean.
Cov(X,Y) = Σ(X − X̄)(Y − Ȳ) / N
- If X is above its mean when Y is also above its mean, the products are mostly positive, and so is the covariance.
- If one tends to be above its mean when the other is below, the covariance is negative.
The sign of the covariance sets the sign of the correlation coefficient r.
Example
In NCERT's farmers example (years of schooling vs yield per acre), the sum of the products of deviations is +42. This positive covariance gives a positive r = 42/(√112·√38) = 0.644. It shows that more schooling goes with higher yield.
Don't confuse with
- Correlation coefficient (r): covariance carries the units of X × Y, so its size is hard to judge. Dividing it by σx·σy gives r, which has no units and lies between −1 and +1.
Related concepts
- Measures of central tendency
- Arithmetic mean
- Weighted arithmetic mean
- Median
- Quartiles
- Decile
- Percentiles
- Mode
- Bimodal and multimodal distribution
- Modal class