EDLC 606
LEARNING ACTIVITY: STATISTICS EXERCISES STUDENT TEMPLATE
Type your answers directly in the document in the spaces provided. Please consider
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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.20,18,17 18.2 18 1
7
1.1
7
3
,17,19
b.15,10,7, 8.4 7 4 3.8
3
1
1
6,4
c.28,28,28 28 28 2
8
0 0
,28,28
d. 19.33 8.5 1
0
26.7
7
7
5
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)?
Distribution (d) includes an extreme outlier (79) that is far from the rest of the
scores. That unusually large value dramatically increases the amount of spread in
the data, causing the standard deviation to increase sharply.
b. Why is the mean so much higher in (d) than in (b)?
Because the mean is sensitive to extreme values, the single high outlier (79)
pulls
the average upward. Even though the rest of the numbers in (d) are similar
to
those in (b), that one large value raises the overall mean
substantially.
c. Why is the median relatively unaffected?
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The median is resistant to outliers. Since it simply represents the middle
position
of ordered scores, the extremely high value at the end of the distribution does
not
change the center
position.
d. Which measure of central tendency best represents the set of scores in (d)?
Why?
The median is the most representative measure of central tendency for
distribution
(d). The extreme outlier distorts the mean but does not influence the
median,
making the median the most accurate reflection of a “typical”
score.
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
Q1=81.75
Q3: 99
Semi-IQ......(Q3-Q1)/2 or 99-81.75/2= 8.63
4. (24 pts, 2 pts each) Fill in the blanks on the table with the appropriate raw scores,
zscores, T-scores, and approximate percentile ranks. You may refer to the distribution
curve below.
Note: the Mean = 50, SD = 5.
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RAW z T Percentile
40 -2 30 2.28
-- 2.5 75 99.38
35 -3 35 0.13
55 1 60 84.13
5. (6 pts, 3 pts each) The following are the means and standard deviations of some
wellknown 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? z = (275-300)/75=-0.333
Test A score = 250+(-0.33 x 4)= 249
b. (3 pts) A score of 400 on Test A corresponds to what score on Test C? z = (400 – 300) / 75 = 1.333
Test C score = 40 + (1.333 x 12) = 56
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.
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a. (2 pts) What percentage of the persons who take the test score below 600?
2.28%
b. (2 pts) Type the curve best representing your answer: Left-tail curve shaded up to
z = –2
c. (2 pts) What percentage of the persons who take the test score below 1200?
84.13%
d. (2 pts) Type the curve best representing your answer: Normal curve shaded up to
z = +1
e. (2 pts) Above what score do the top 2.27% of the test-takers score? 1400
f. (2 pts) Type the curve best representing your answer: Right-tail curve at z = +2
7. (14 pts, varied) Refer to the following data and scatterplots to respond to questions 7a-e.
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Individua
l 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
10 12 14 16 18 20 22 24
0
5
10
15
20
25
30
35
40
Figure A
Years of School
Body Mass Index
10 12 14 16 18 20 22 24
0
5
10
15
20
25
30
35
40
Figure B
Years of School
Body Mass Index
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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? Negative. As years of
schooling increase, BMI tends to decrease.
b. (2 pts.) Estimate the strength of the correlation coefficient: Approximately
moderate. Around –0.5 to –0.6
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?
The correlation becomes stronger and more consistently negative because the
highschooling individuals cluster around lower BMI values with fewer exceptions.
d. (4 pts.) Explain why this is the case.
Removing individuals with fewer years of schooling eliminates much of the variability
that weakens the overall trend. The remaining data points show a clearer pattern:
more
education corresponds to lower BMI, resulting in a tighter, more linear
relationship.
e. (4 pts.) Identify how likely it is that a causal relationship has been indicated. A
causal relationship is unlikely. While the two variables are associated, many
outside factors—such as diet, income, exercise, genetics, and access to
Consider Figure D (below).
10 12 14 16 18 20 22 24
0
5
10
15
20
25
30
35
40
Figure D
Years of School
Body Mass Index
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healthcare—also influence BMI. Correlation alone cannot establish that years of
schooling cause lower
BMI.
