Question

please explain what’s variance and why it use square and not absolute value

Answer 1

Answer: In Statistics, population variance (σ²)  is a measurement of the spread between the numbers in a population. Thus it measures how far each number in the population set is from the mean and therefore from every other number in the set.

The formula of the population variance is σ² = (sum(xi - mu)²)/N where the sum runs from i=1(1)N, N being the population size, xi = the ith data point, mu = population mean.

The population variance is estimated by the sample variance (s²).

The formula of the sample variance is s² = (sum(xi - xbar)²)/(n-1) where the sum runs from i=1(1)n, n being the sample n size, xi = the ith data point, xbar = sample mean.

Thus, the variance of a dataset is calculated by taking the arithmetic mean of the squared differences between each value and the mean value. Squaring the differences has some advantages, these are as follows --

a) Squaring the differences make each term positive so that the values above the mean do not cancel the values below the mean

b) Squaring the differences add greater weight to the larger differences, and in the cases where the points further from the mean are more significant, this weighing is appropriate.

c) Also, there is ease in statistical calculations when we square the differences and use that measurement.