Question

What are the four steps to calculate the variance (typically of a sample if done by hand)?

Answer 1

To calculate the variance of a sample, find the sample mean, compute the squared deviations of each data point from the mean, sum these squared deviations, and divide by the number of observations minus one.

Step-by-step explanation:

To calculate the variance of a sample, follow these four steps:

1. Calculate the sample mean (x-bar). Sum all the data points and divide by the number of data points (n).
2. Compute the deviations. Subtract the sample mean from each data point and square the result.
3. Sum up the squared deviations. This gives you the total variance for the data set.
4. Divide the sum of squared deviations by the number of observations minus one (n-1). The result is the sample variance (s²).

It's important to remember that when calculating the variance for a sample, you divide by n-1 to account for the degrees of freedom in the estimate. If calculating the variance for a population, you would divide by N, the total number of observations. In practice, especially with large data sets or more complex calculations, using a calculator or statistical software can save a significant amount of time and reduce the possibility of errors.