Variance describes how far the numbers lie from the expected value. In simple words it is the amount of variation. Here the expected value is the Mean. Variance is the average of the squared differences from the mean.
Where μ is the mean
N is the total number of values
For continuous random variable,
Var (x) = ∫ (x- μ)2 f(x)dx
Where μ is the expected value.
μ = ∫ x f(x)dx
Variance is also defined as the difference of mean of square and square of mean.
If x is the random variable which has a an expected value μ = E[x]
Var(x) = E [(x-μ)^2]
= E [x² -2μx+μ²]
= E [x²] -2μ E[x] + μ²
= E[x²] -2μ² + μ²
= E[x²] - μ²
= E[x²] – (E[x])²
Example 1: Six students from a class weigh 53 kg, 63kg, 92kg, 43kg, 39kg, 64kg. Find the variance of the weight of the students (Round of to two decimal places)
Example 2: Edward has 5 dogs. Their heights are 550mm, 250mm, 149mm, 175mm,146mm. Find the variance (Round of to 1 decimal place).