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