As the draws spread out from the mean (both above and below), the variance increases. Since some observations are above the mean and others below, we square the difference between a single observation (k _i) and the mean (μ) when calculating the variance.

Does variance change with mean?

Adding a constant value, c, to a random variable does not change the variance, because the expectation (mean) increases by the same amount. ... The variance of the sum of two or more random variables is equal to the sum of each of their variances only when the random variables are independent.

Does variance increase or decrease with sample size?

Therefore, when drawing an infinite number of random samples, the variance of the sampling distribution will be lower the larger the size of each sample is.