Study Guide Packet 1, Chapter 5
Z-Score Activity
1. The researcher found that stress ratings varied per person and wanted to reach out to those most
stressed and least stressed to find out why. However, all the data are based on different scales (for
example two scales were “out of 100 points” while the other was “out of 200 points”). The higher
the scores on each scale indicate more stress, but the only way to compare all data would be to
calculate Z scores to see how many standard deviations (SD) points each student’s score (X) is
from the mean (M) of their group. Calculate the three random students’ Z scores and report who
is “most stressed” and “least stressed”.
To find the Z score that corresponds to a raw score, use the following formula.
X is “score”, M is “mean” (average), SD is Standard Deviation (sometimes seen as just S)
Student A
X = 10
M = 60
SD = 10
Z = -5
Student B
X = 75
M = 50
SD = 5
Z = +5
Student C
X = 110
M = 100
SD = 20
Z = +.5
The student who is MOST stressed is Student Student B
The student who is LEAST stressed is Student Student A
2. What if it’s the Z score we know and we want to find out what the raw score was?
To find the raw score that corresponds to a Z score, use the following formula.
Z is “Z score”, SD is Standard Deviation (sometimes seen as just S), M is “mean” (average)
Student D
Z = 2.0
SD = 10
M = 150
X = 170
Student E
Z = -1.5
SD = 5
M = 100
X = 92.5
Student F
Z = 1.0
SD = 20
M = 70
X=
90