In statistics, the variance of a random variable is a measure of how its values are distributed. The variance is calculated by taking the average of the squared differences of each value from the mean. This is known as the squared deviation, or the square of the deviation of each value from the mean. The square of the deviation is used because it emphasizes the differences between values that are farther away from the mean. This makes the variance a measure of dispersion, or how much the values of the random variable spread out from the mean.

What is the square of the variance?

The square of the variance is a measure of the spread of data points in a dataset. It is calculated by taking the sum of the squared differences between each data point and the mean of the dataset, and then dividing by the total number of data points. Mathematically, it is expressed as:

Variance = ∑ (x – μ)2/N

where x is a data point, μ is the mean of the dataset, and N is the total number of data points.

Why is variance sum of squares?

The variance sum of squares (SS) is a measure of the total variability of a set of data points around their mean. It is calculated by summing the squared differences between each data point and the mean. The larger the variance SS, the more spread out the data points are from their mean. This measure is useful for comparing the variability of different datasets and determining how much of the variability is due to random chance or to actual differences in the data.