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SYA Chapter 5
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Student A and Student B are
taking Introduction to Sociology courses
taught by different instructors. Each student
earned 76 out of 100 points in their midterm
exams. The course average was 70 in both
courses.
Are these students performing
equally?
use the z formula
the z score formula allows you to...
convert original scores to z scores.
What is going on in the z-score conversion?
- You first compute the score's distance from the mean.
Then convert the distance into the unit of standard deviation.
Convert the two test scores in the previous slide into z-scores.
Student A: (76-70)/3=2
Student B: (76-70)/12=.5
12 and 3 are the sigmas. Now it is clear that Student A has a higher z score.
Z = 0:
The student got the average.
Z = 2:
The student is 2 standard deviations above the mean.
Z = -1:
The student is 1 standard deviation below the mean.
z-scores help you to describe the...
relative position of each score in the distribution.
What do we mean by "standardizing a distribution"?
You convert everyone's score into z score.
Note that you can standardize distributions of any shape. After standardization...
the shape will stay the same as the original.
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