I have dataset with 61 entries. What i am trying to do is to calculate variance.
I am doing it with two ways but they differ
1st way is following
$var X = E(X^{2}) - (EX)^{2}$
so
> c = 0
> for( year in females$Salary )
+ c = c + (year^2)
> (c/length(females$Salary) - mean(females$Salary)^2
[1] 286682.3
but when i use build in function
> var(females$Salary)
[1] 291460.3
as u can see the output is different. Why is this happening? Shouldnt they be the same?
var in R uses the unbiased estimator of the variance (sample variance) which has a denominator of n-1.
Your calculation uses the formula of variance.
Check this:
vec <- 1:100
#var uses the sample variance where the denominator is n-1 i.e. 99
var(vec)
#[1] 841.6667
1 / 99 * sum((vec - mean(vec))^2)
#[1] 841.6667
#this is what you use to calculate variance, which uses a denominator of n i.e. 100
mean(vec^2) - mean(vec)^2
#[1] 833.25
1 / 100 * sum((vec - mean(vec))^2)
#[1] 833.25
