Data Matters with Excel®

Activity 7.2

If you only had the sample means available, could you figure out the standard deviation of the population they came from?

To get you started, here is the relationship between the standard deviation of sample means (the standard error) and the standard deviation of the population from which the observations were drawn.

It would seem that you could multiply both sides by the square root of the sample size and get

To put it the other way,

Does that work? If you have only the sample size and some sample means, can you accurately estimate the population standard deviation?

To find out, you will take random samples of the Rep US Sample. Find their means and the standard deviation of the sample means. Multiply what you get by the square root of your sample size. Then check if you got a good estimate of the population standard deviation.

Use the same strategy that you used in the project in Section 6.3. Open that workbook. In that project, you took random samples and calculated their means. Their means are on the Stats worksheet. You could collect some more sample means or just work with those.

To get the standard deviation of those means, select a blank cell, type =stdev( , select the sample means, type ) , and press “Enter.”

That gives you the standard deviation of the sample means, which is an estimate of the standard error. Multiply that by the square root of the sample size to estimate the population standard deviation.

Open the Data worksheet and use the same method to calculate the standard deviation of the column of data that your sample was drawn from.

How did you do? Was your estimate a good estimate?

Does it matter what the sample size is? Does it matter how many samples you work with?

What if different samples had different sizes? Could you use this equation if different samples had different sizes?