Question 181:

Asked on May 5, 2008

Tags: Standard Deviation , Degrees of Freedom

1

Answer:

No answer provided yet.

The population standard deviation is the actual variability of all members of a group--the population, such as the variability of IQ scores for all 8th graders in the US. As is the case with most population parameters, we don't know what they are, since we haven't actually measured the IQ of all 8th graders in the US. Instead, we have to estimate the standard deviation using some sample of 8th graders. But to calculate the standard deviation (and also the variance) we need to know the population mean, which we also don't know! This leads to the two main calculation differences between the sample SD and population SD.

For the population standard deviation, you:

1. subtract each value in the population from the population mean
2. square the difference value
3. add up all the squared difference values
4. divide the sum by the sample size
5. take the square root

In the sample standard deviation you:

1. subtract each value from the sample mean
2. square the difference value
3. add up all the squared difference values
4. divide the sum by the sample size minus 1
5. take the square root

You'll notice the two differences are using the population mean for the population standard deviation, and divide by the sample size. Since we do not know the population mean, the sample size is penalized, so to speak, and 1 value is subtracted from the sample (called a degree of freedom). I've explained the formulas above, if you'd like to see them in hard-to-understand notation, just look in any statistics text or there's a thorough explanation on Wikipedia.