does "mean score" and "sample mean" mean the same thing?

Question

You take an exam with 400 possible points and are told that the mean score is 280 and that the standard deviation is 20. You are also told that you got 350. Did you do well on the exam? Just trying to get my old mind around the statistics concepts.

Answer 1

John,

 

The mean score and standard deviation characterizes the distribution from which you are drawing a finite sample randomly (no dependence from one draw to any other draw).  Based on your total sample size n, the calculated sample mean is your estimate of the mean score.  In general, you won't hit it on the head with any sample, but repeated samples will produce computed values that cluster around and near the true mean score.

 

In your example, you got 350 on the exam which is a normalized (z=[350 - 280]/20) 3.5 standard deviations above the mean score.  If that is approximated by a normal distribution, then the probability that any grade on that exam will exceed yours is about 0.0002.  So you did extremely well on the test.