EDLC 606
LEARNING ACTIVITY: STATISTICS EXERCISES STUDENT TEMPLATE
Type your answers directly in the document in the spaces provided. Please consider highlighting,
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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. 18.2 18 17 1.17 3
b. 8.4 7 n/a 3.83 11
c. 28 28 28 0 0
d. 19.3 8.5 10 26.77 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)?
Because d has 79 which is the largest number in the groups and no other numbers
are close.
b. Why is the mean so much higher in (d) than in (b)?
Because d has 79 which is the largest number in the groups and no other numbers
are close.
c. Why is the median relatively unaffected?
Because it searches for the middle number.
d. Which measure of central tendency best represents the set of scores in (d)? Why?
There is not one due to the outlier of 79 there is not a number that can represent it
along with all the other numbers that are much lower.
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
Q2= 99
SIR= 8.63
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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 30 2.28
62.5 2.5 75 97.72
42.5 -1.5 35 6.68
60 2 70 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
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EDLC 606
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___
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 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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EDLC 606
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: e___
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: _b__
e. (2 pts) Above what score do the top 2.27% of the test-takers score? __93_
f. (2 pts) Type the curve best representing your answer: _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
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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
EDLC 606
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__
b. (2 pts.) Estimate the strength of the correlation coefficient: ___strrong
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
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?
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EDLC 606
The correlation coefficient measures the strength and direction of a linear
relationship between two variables. In this case, the variable of interest is the
years of school and the body mass index (BMI). If we focus only on the data
points where the years of school are above 16, this may affect the correlation
coefficient.
d. (4 pts.) Explain why this is the case.
Focusing on data points with years of school above 16 could lead to a higher correlation
coefficient. This is because it seems like there might be a negative correlation between
years of school and BMI in the given data. That is, as years of school increase, BMI tends
to decrease. By excluding data points where years of school are below 16, which might
be outliers, the negative correlation could be more pronounced, affecting both the
direction and strength of the correlation coefficient.
e. (4 pts.) Identify how likely it is that a causal relationship has been indicated.
Correlation does not imply causation. Even if a correlation is observed between years of school
and BMI, it does not necessarily mean that one variable causes the other. There could be
confounding variables or other factors influencing the relationship. Additionally, it's important to
note that correlation does not provide information about the direction of causation. In this case, it
is not clear whether higher education causes lower BMI or the other way around.
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