EDLC 606
Learning Activity: Statistics Exercises Student Template
Type your answers directly in the document in the spaces provided. Please consider highlighting, starring*, or changing the font color of answers for ease of instructor grading. You MUST show your work to be eligible for partial credit.
1. (20 Pts, 1 pt each). Calculate the mean, median, mode, standard deviation, and range for the following sets of measurements (fill out the table):
a. 20, 18, 17, 17, 19
b. 15, 10, 7, 6, 4
c. 28, 28, 28, 28, 28
d. 10, 10, 7, 6, 4, 79
DISTRIB
MEAN
MEDIAN
MODE
SD
RANGE
a.
b.
c.
d.
2. (20 Pts, 5 pts each) Answer the following questions.
a. Why is the SD in (d) so large compared to the SD in (b)?
b. Why is the mean so much higher in (d) than in (b)?
c. Why is the median relatively unaffected?
d. Which measure of central tendency best represents the set of scores in (d)? Why?
3. ( 4 pts) Determine the semi-interquartile range for the following set of scores.
92 95 89 65 99 100 85 67 72 99 85 100
4. (24 pts, 2 pts each) Fill in the blanks on the table with the appropriate raw scores, z-scores, T-scores, and approximate percentile ranks. You may refer to the distribution curve below.
Note: the Mean = 50, SD = 5.
RAW
z
T
Percentile
40
2.5
35
84.13
5. (6 pts, 3 pts each) The following are the means and standard deviations of some well-known standardized tests, referred to as Test A, Test B, and Test C. All three yield normal distributions.
Test
Mean
Standard Deviation
Test A
300
75
Test B
250
4
Test C
40
12
a. ( 3 pts) A score of 275 on Test A corresponds to what score on Test B? ____
b. ( 3 pts) A score of 400 on Test A corresponds to what score on Test C? ____
6. (12 pts, 2 pts each) The Graduate Record Exam (GRE) has a combined verbal and quantitative mean of 1000 and a standard deviation of 200. Scores range from 200 to 1600 and are approximately normally distributed. For each of the following problems, indicate the percentage or score called for by the problem and select the appropriate distribution curve (from below) that relates to the problem.
a. ( 2 pts) What percentage of the persons who take the test score below 600? ___
b. ( 2 pts) Type the curve best representing your answer: ___
c. ( 2 pts) What percentage of the persons who take the test score below 1200? ___
d. ( 2 pts) Type the curve best representing your answer: ___
e. ( 2 pts) Above what score do the top 2.27% of the test-takers score? ___
f. ( 2 pts) Type the curve best representing your answer: ___
7. (14 pts, varied) Refer to the following data and scatterplots to respond to questions 7a-e.
Individual
Years of School
Body Mass Index
A
21
18
B
18
20
C
17
33
D
17
29
E
14
31
F
11
32
G
22
19
H
23
21
I
16
33
J
22
36
K
17
30
L
15
28
M
17
20
N
12
28
O
14
33
P
13
29
Figure A represents a scatterplot constructed from the data; Figure B represents a regression line drawn through the scatterplot that “fits” the data points reasonably well; Figure C represents an ellipse drawn around the data points.
a. ( 2 pts.) What is the overall direction of the correlation? ___
b. ( 2 pts.) Estimate the strength of the correlation coefficient: ___
Consider Figure D (below).
c. ( 2 pts.) Using only the data points associated with the years of school above 16; what effect does this have on the direction and strength of the correlation coefficient?
d. ( 4 pts.) Explain why this is the case.
e. ( 4 pts.) Identify how likely it is that a causal relationship has been indicated.
Figure A
Body Mass Index 21 18 17 17 14 11 22 23 16 22 17 15 17 12 14 13 18 20 33 29 31 32 19 21 33 36 30 28 20 28 33 29
Years of School
Body Mass Index
Figure B
Body Mass Index 21 18 17 17 14 11 22 23 16 22 17 15 17 12 14 13 18 20 33 29 31 32 19 21 33 36 30 28 20 28 33 29
Years of School
Body Mass Index
Figure C
Body Mass Index 21 18 17 17 14 11 22 23 16 22 17 15 17 12 14 13 18 20 33 29 31 32 19 21 33 36 30 28 20 28 33 29
Years of School
Body Mass Index
Figure D
Body Mass Index 21 18 17 17 14 11 22 23 16 22 17 15 17 12 14 13 18 20 33 29 31 32 19 21 33 36 30 28 20 28 33 29
Years of School
Body Mass Index
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