We take a random sample of four people and measure their heights ( in inches). The sample mean and variance are 67 and 3.6, respectively. A fifth person whose height is 67 is added in the sample. What is the new sample variance?

Well we know that we have: sum of((x(i)- x(avg))^2)/(n-1)

So the first time we has 3.6= Y/(4-1). Where Y=sum of((x(i)- x(avg))^2)

So Y= 3.6 * 3= 10.8

Now Y has another variable in it that we need to add on so:

Y + (67-x(avg))^2

Y + (67-67)^2

Y+0

So now we take Y and divide it by n-1

Y/(5-1)

10.3/(5-1)=2.7