You are Here: Home >< Maths

# S3 Estimation watch

1. Hey guys,

Im currently reading about unbiased estimators which I think is when you use the distribution of samples to estimate the mean and standard deviation of a population. Please correct me if I'm wrong.

I've understood the proof that shows that E(X bar) = u (population mean)
and Var(X bar) = sigma squared over n
Now I'm coming across another formula for Variance= (?X^2-nXbar^2)/n-1
Is this equivalent to sigma squared over n? Is it called the sample variance, like ?X/n is called sample mean?

Also, can someone please explain this concept of bias to me? Whats the difference between a biased and unbiased estimator? If an estimate of E(X bar) wasn't equal, to "u" this wouldn't necessarily mean it was biased would it?

Sorry, im just really confused with these concepts and am trying to self teach this module :/ If you know of any good websites to get help with s3 please let me know.
thanks
2. If the expected value of an estimator is equal to a population parameter then we say that the estimator is unbiased.

It can be proved that if S^2= (n/n-1)*(sum X^2/n - (Xbar^2)) or equivalently (?X^2-nXbar^2)/n-1 as you write,

then E(S^2)= sigma, the population variance. So S^2 is an unbiased estimator for the population variance sigma.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 20, 2011
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams