From: "Thaddeus J. Evert" Newsgroups: sci.math Subject: Re: Z Score HELP Date: Wed, 30 Sep 1998 02:25:01 -0500 On Wed, 30 Sep 1998, Bob wrote: > Can anyone help me with the definition na d application of Z Scores > For a set of values M = the mean (or average) of the values S = the standard deviation of the values x = the value in question then the z-score of x is z = (x - M)/S The z-score can, when compared against a table of z-scores and/or fed into a calculator, indicate the probability of how likely an event is. For instance, let's say you have a set of grades on a test from a given class that had a somewhat "normal" distribution: 50 60 65 67 70 71 72 73 74 75 75 76 76 77 77 78 78 79 79 80 80 81 81 82 82 83 83 84 84 85 86 87 88 89 90 93 95 100 The mean is M = 3005/38 = 79.07894736842... S = 9.45939138362... Assuming this distribution, you want to know the probability of making 90 or above on the test. z = (x - M)/S = (90 - 79.1)/(9.46) = 1.15 Looking this score up in a table tells you the probability of getting a 90 or better on a test like this is 1 - (0.5 + 0.3729) = 0.1251 or roughly 12.51%. In general, if a sample of values tend to assume a normal distribution (which many do) you can use z-scores to compute the probabilities of future occurences of vales within a given range. The applications of this are almost limitless: analysis of data with "error" quality control voting patterns weather forecasting marketing "curving tests" and much, much more... Keep an open mind, Thaddeus \O/ _| \ / |_ \0/ | __\0 \_ | _/ 0/__ | / \ | \ |0 /0\ 0| / | / \ "The time you enjoy wasting is not wasted time. - Bertrand Russell