Statistics for People Who (Think They) Hate Statistics
Statistics for People Who (Think They) Hate Statistics
Some questions in Part A require that you access data from Statistics for People Who (Think They) Hate Statistics. This data is available on the student website under the Student Text Resources link.
1. Why is a z score a standard score? Why can standard scores be used to compare scores from different distributions?
A z score is considered a standard score because it is based on the degree of variability within its distribution. Standard scores across different distributions measure in the same fashion. A z score is the result of dividing the amount that a raw score differs from the mean of the distribution by the standard deviation. So, scores below the mean will have negative z scores, and scores above the mean will have positive z scores. Positive z scores always fall to the right of the mean, and negative always fall to the left (Salkind, 2011).
2. For the following set of scores, fill in the cells. The mean is 70 and the standard deviation is 8.
Raw score
Z score
68.0
-0.25
57.2
–1.6
82.0
1.5
84.4
1.8
69.0
–0.125
66.0
–0.5
85.0
1.875
83.6
1.7
72.0
.25
3. Questions 3a through 3d are based on a distribution of scores with image2.png and the standard deviation = 6.38. Draw a small picture to help you see what is required.
a. What is the probability of a score falling between a raw score of 70 and 80? 0.5668
b. What is the probability of a score falling above a raw score of 80? 0.2166
c. What is the probability of a score falling between a raw score of 81 and 83? 0.0686
d. What is the probability of a score falling below a raw score of 63? 0.0300
4. Jake needs to score in the top 10% in order to earn a physical fitness certificate. The class mean is 78 and the standard deviation is 5.5. What raw score does he need? (x-78) / 5.5 = .9 Minimum required score of 85.04
5. Who is the better student, relative to his or her classmates? Use the following table for information.
Math
Class mean
81
Class standard deviation
2
Reading
Class mean
87
Class standard deviation
10
Raw scores
Math score
Reading score
Average
Noah
85
88
86.5
Talya
87
81
84
Z-scores
Math score
Reading score
Average
Noah
2
0.1
1.05
Talya
3
-0.6
1.2
