Two statistics problems?

Question

1) What is the difference between population standard deviation and sample standard deviation? Why is this distinction made?

2)1) A tire manufacturer wants to determine the inner diameter of a certain grade of tire. Ideally, the diameter should be 570 millimeters. The data is as follows:

572,572,573,568,569,575,565,570
Can you comment on the quality of the tires.
based on mean and S.D

I know how to find mean and s.d. how can I make a comment on the quality of tyres

Answer 1

1. Population standard deviation means the s.d. of all the things that you are interested in. In part 2 this would be all tyres of that type that the manufacturer makes. Sample standard deviation means the s.d. actually calculated from measured results. The latter would be used as an estimate of the former in cases where the population is so large that it is impossible or prohibitively expensive to measure every member of the population.

2. The tyres would be of good manufacture if two things are true. Firstly the mean of the sample is close to the mean that it is supposed to be for the population. How close is a matter of judgement. Secondly the s.d. is small, indicating that there is not much variation among the population. Again how small is a matter of judgement. For instance the variation acceptable for cheap children's bicycles would be a bit larger than that for F1 racing cars.

Answer 2

An excellent explanation with a good example is given here
http://en.wikipedia.org/wiki/Standard_deviation