Z Scores

Z scores are standardized scores that compare the distance between the data point and the mean with the standard deviation.

Z Score = (measurement - mean)/ standard deviation

A negative z score indicates measurement is smaller than the mean while a positive z score says that the measurement is larger than the mean.

Example:  A teacher gives a test and the class average is 74 with a standard deviation of 6.
                A particular student scores an 88 on the test giving a z score of

z score = (88 - 74)/ 6  = 2.33
this student scored 2.33 standard deviations above the mean

               A second student scores a 70 on the same test.  That student has a z score of

z score = (70 - 74)/6 = -.67
This student scored .67 standard deviations below the mean