# Thread: expected value, standard deviation

1. ## 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.

2. 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.

3. 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