Z-scores, also called standard scores, describe the position of a raw score in relation to the mean of a distribution using standard deviation as the measurement unit. A positive z-score indicates a value above the mean, while a negative z-score is below the mean. In the examples provided, Student A had a z-score of 3, meaning their score was 3 standard deviations above the mean and higher than Student B's score of -2 standard deviations below the mean. Fred also scored better on Test B with a z-score of 2 compared to 1 on Test A. The document provides examples of calculating and interpreting z-scores.

2.  z-scores are also called "STANDARD
SCORES".
 A z-score states the position of a raw
score in relation to the mean of the
distribution, using the standard
deviation as the unit of measurement

3.  50% of scores fall below the mean.
 50% of the scores are above the mean.

4. (Student A ) z- score= 3
(Student B) z- score= -2
STUDENT A
STUDENT B
Therefore:
Student A is 3 standard deviations above
the mean
Student B is -2 standard deviations
below the mean

5.  The z-score is POSITIVE if the data value lies
above the mean and NEGATIVE if the data
value lies below the mean.
Conclusion: Student A performed better than Student B.

7. SOLUTION:

8.  Fred’s z-score inTEST A = 1
 Fred’s z- score inTEST B= 2
Conclusion: Fred did better on TEST B, because
he is 2 standard deviations away above the
mean

9. Another Example:
Lets have another example, Lets say
you took a final exam and scored 80.
The mean score for the exam is 70 and
the standard deviation is 3. How well
did you score on the test compared to
the average test taker?

10. FINALTEST
Score: 80
Mean: 70
Standard deviation: 3
Using the formula:
Z-score= 80 – 70 / 3 = 3.3
Z- score= 3.3
 This means that your score was 3.3
standard deviations above the
mean. Therefore we can say that
you performed better compared to
the average test taker.

11. Example:
Find the value represented by a z- score of
2.403.
Given;
Mean- 63
Standard deviation- 4.25
Solution:
2.403= x – 63 / 4.25
10. 213= x – 63
X = 73. 213
73.213 has a z- score of 2.403

12. A group of data with normal
distribution has a mean of 45. If one
element of the data is 60, will the z-
score be positive or negative?
Question:
The z-score must be positive since
the element of the data set is
above the mean.

13. To sum it up, z scores gives
clarity and comparison on a
given data set because of the
fact that you can see and
understand the relationship
between the raw score and
the distribution of scores
much clearer.

14. That’s all!
Thank you for watching !