Question

Mike, Tania, Bill, and Rachel each took many samples from the same population of students. The number of students in each of their samples is shown in the table below. Which person's sample means probably showed the least variability?

Person taking the sample: Mike Tania Bill Rachel
# of students in each sample: 23 37 79 51

Answer 1

The standard deviation of the sample means is given by:
\[\large \frac{\sigma}{\sqrt{n}}\]
where sigma is the population standard deviation and n is the sample size.
You should be able to use the above formula to find the person whose sample means probably showed the least variability.

Answer 2

oh ok how do i know the standard deviation so i can use the formula then?

Answer 3

You do not need to know the value of the population standard deviation, the reason being it is the same value for the calculation of the standard deviation of the sample means for each person. For example the standard deviation of the sample means for Mike is:
\[\large \frac{\sigma}{\sqrt{23}}\]
and for Tania it is:
\[\large \frac{\sigma}{\sqrt{37}}\]
Therefore you can see which person's standard deviation of the sample means has the lowest value.

Answer 4

ok so with just calculating the bottom numbers i got that Bill would have the lowest because your dividing by the biggest number, does that sound like the right way to do it or still no?

Answer 5

Yes, you are correct.

Answer 6

Thanks!

Answer 7

You're welcome :)