Covariance Calculator

How it is calculated

Enter the X list and the Y list; values can be separated by commas or spaces. They must have the same count, at least two pairs, and every item must be a number. The tool finds the two means, multiplies each pair of deviations and adds them: S = Σ (xi − x̄)(yi − ȳ). Sample mode divides by n − 1, population mode divides by n. A mode other than population is treated as sample. The result is rounded to two decimals, so a very small covariance such as that of values near 0.001 shows as 0.00. The unit is the unit of X times the unit of Y. The tool also shows the number of pairs. It does not give a correlation coefficient. Row order matters, because values are paired by position.

Common mistakes

• Typing a decimal comma in a list, such as 3,1 for 3.1. A comma separates values, so 3,1 becomes two numbers and the pair count no longer matches.
• Giving lists of different length, or a text entry like x in the list. Either returns no result.
• Choosing population mode for data that is only a sample. Population mode divides by n, so the figure is smaller than the sample one, here 1.30 instead of 1.63.
• Reading covariance as the strength of a relationship. Its size depends on the units, so use correlation to compare relationships, and only the sign tells the direction.
• Entering the X and Y values in different orders. They are paired by position, so a shuffled Y list gives a different and meaningless answer.