EDLC 606
LEARNING ACTIVITY: STATISTICS EXERCISES STUDENT TEMPLATE
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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. 18.2 18 17 1.16 3
b. 8.4 7 None 3.82 11
c. 28 28 28 0 0
d. 19.33 8.5 10 26.76 75
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)?
The standard deviation is larger due to the mean scores of (b) being smaller in
measurements than in (d), which are larger in measurements.
b. Why is the mean so much higher in (d) than in (b)?
The mean is higher in (d) due to the score of 79, which skews the mean as
compared to (b), which is relatively closer to the measurement values in the set.
c. Why is the median relatively unaffected?
The median is relatively unaffected because it doesn’t consider the outliers in a
dataset, as it represents the middle value of the dataset.
d. Which measure of central tendency best represents the set of scores in
(d)? Why? The median best represents the central tendency because most of the
dataset is relatively close to 8.5. This is because it does’ take into account the
outliers of the score “79” as we are accounting for the central measurement, we can
assume that a graph would be skewed because of this number. Also, the mean and
mode are relatively close to one another, which would indicate that most of the
dataset would be closer to one of these numbers.
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
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Q1: 85+72=157/2 = 78.5
Q3: 99+99=198/2= 99
99-78.5/2= 10.25
Answer: 10.25
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.
RAW z T Percentile
40 - 2 30 2.3
62.5 2.5 75 99
42.5 -1.5 35 6.8
55 1.0 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? 248.67 ____
b. (3 pts) A score of 400 on Test A corresponds to what score on Test C? 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
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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?
_2.27__
b. (2 pts) Type the curve best representing your answer: _Curve E__
c. (2 pts) What percentage of the persons who take the test score below 1200?
_84.12__
d. (2 pts) Type the curve best representing your answer: _Curve C__
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: _Curve B__
7. (14 pts, varied) Refer to the following data and scatterplots to respond to questions 7a-e.
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
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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? __The overall direction of
the correlation is a moderate negative correlation._
b. (2 pts.) Estimate the strength of the correlation coefficient: _-0.308 Consider
Figure D (below).
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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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 direction may change from positive to negative due to the
truncated range available for selection, and the correlation strength may also
weaken.
d. (4 pts.) Explain why this is the case. If we are looking at the whole data set, we
can correlate that with increased years of school, the BMI increases as well. By
limiting our view to 16 years of schooling and beyond, the data set will be
truncated, giving us a false sense of BMI dispersion, which correlates to a weaker
strength.
e. (4 pts.) Identify how likely it is that a causal relationship has been indicated. The
correlation between the two doesn’t show a causal relationship, as shown by the
scatterplot. This is due to the unknown variables that went into the scatterplot.
There can be either a negative or a positive correlation between BMI, which
decreases or increases for personnel with more than 16 years of schooling.
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
