Keep in mind that you're dealing with a random variable. There is variation. I wrote some code to simulate this process

The results are at the bottom. So on average if you do this experiment the unbiased result will be 2.5 and the biased result will be 2.25.Code:`experiment <- function(n, k = 10){ # Flip a coin k times and count the number of heads, do that n times vals <- rbinom(n, k, 0.5) # This gives the unbiased estimate of variance sampvar <- var(vals) # Need to multiply by (k-1)/k to get the biased estimate popvar <- sampvar * (k-1)/k # Return the results result <- c(unbiased = sampvar, biased = popvar) return(result) } # Do the experiment where you flip a coin 10 times and repeat that 200 times... # But do that whole process 1000 times and record the results test <- replicate(1000, experiment(200, 10)) # > summary(test["unbiased",]) # Min. 1st Qu. Median Mean 3rd Qu. Max. # 1.789 2.329 2.494 2.500 2.660 3.552 # > summary(test["biased",]) # Min. 1st Qu. Median Mean 3rd Qu. Max. # 1.610 2.096 2.244 2.250 2.394 3.197`