Variance Calculation

Calculate the variance of a series of numbers

How to calculate the variance?

Variance is a measure of spread that indicates the average squared deviation of the mean value of a series of numbers. It's one of the most used measures in statistics, as it provides an insight into how data vary around the average. Variance can be used in risk assessment, quality control, and a wide range of quantitative research methods.

Steps to calculate the variance

Calculating variance is a process that consists of various steps:

1. Calculate the mean (or average value) of the series of numbers: This is the sum of all numbers in the series, divided by the number of numbers in the series. For instance, if you have the series of numbers {4, 8, 6, 5, 3, 2, 8, 9, 2, 5}, the mean is (4 + 8 + 6 + 5 + 3 + 2 + 8 + 9 + 2 + 5) / 10 = 5.2.
2. Subtract the mean from each number in the series and square the result: The deviation of each number in the series from the mean is calculated, then this deviation is squared. This gives the squared deviation of each number.
3. Calculate the average of these squared deviations: This is the sum of all squared deviations, divided by the number of numbers in the series. This result is the variance.

Example

Let's take the following series of numbers as an example: 4, 8, 6, 5, 3, 2, 8, 9, 2, 5.

1. We first calculate the average of the series of numbers, which is 5.2.
2. Next, we subtract the average from each number in the series and square the result. For the number 4 for instance, the calculation would be: (4-5.2)² = 1.44. We do this for each number in the series.
3. The sum of these squared deviations is then 13.6. We divide this by the number of numbers in the series (10) to get the variance. This is 1.36.

Variance gives us a measure of how much the values in the series of numbers are spread around the average. A high variance indicates a large spread of the values, whereas a low variance indicates that the values are close to the average.

It's important to note that, because variance works with squared deviations, the unit of variance is the square of the unit of the original values. Therefore, the square root of the variance is often used, known as the standard deviation, to get the spread of values in the same units as the original values.