# expected value, standard deviation

• Jun 8th 2011, 12:39 PM
Nforce
expected value, standard deviation
We have the population of 3000 students. The average height of this population is 180 cm with the standard deviation of 5 cm. We pick 25 random students and measure their height.

What is the expected value and standard deviation for the average height of this sample?

I was thinking about this, but my conclusion is that the average will be 180cm with 5 cm standard deviation if we pick a sample of 25 students.

I know it's wrong but, can someone explain this with mathematical formulas and philosophical idea behind it.

thank you.
• Jun 8th 2011, 01:28 PM
TKHunny
The expected value of the mean is the mean of the population given that the mean is an unbiased estimator.

The variance of the mean of a sample is greater than zero becuase it is a sample. It should shrink until you have selected the entire population.
• Jun 8th 2011, 11:51 PM
Nforce
I found these formulas, and calculate. Is this correct?

The mean of entire population is equal to the mean of the sample.
So the mean of the sample is = 180 cm.

And standard deviation of a sample is o = o/sqrt(n), o = 5/sqrt(25) = 1