STATISTICS 244.3 (01)
Term Test 1
May, 2007
Open Book Examination: Students are allowed to take into the examination a
calculator, their textbook, and formulae sheets. Each question is worth approximately the
same value (2 marks).
Student Name:
I.
Student No:
In the following study educational researchers were interested in whether a New
Method for teaching mathematics was more effective than the Standard Method. A
sample of 20 students were taught by the Standard Method, while another sample of
15 students were taught by the New Method. Each student was given a mathematics
proficiency test at the end of the teaching period. The scores on this test are tabulated
below:
Standard
Method
New
Method
54.2
76.4
77.5
37.9
61.9
69.6
70.3
23.7
69.2
66.0
63.2
14.5
76.1
81.1
33.4
26.6
55.8 67.3 73.9 67.3 73.9 71.4
66.6 77.2 89.9 85.4 66.3 67.9
55.6 42.0 13.8 10.7 36.9 71.6
55.2
Some Summary Statistics are given below:
n
x
x2
Standard
Method
New
Method
20
1417.4 101932.70
15
632.9
33669.55
Answer
1. Determine the mean of math proficiency scores of students taught by the Standard
Method.
2. Determine the median of math proficiency scores of students taught by the New
Method.
3. Determine the median of math proficiency scores of students taught by the Standard
Method.
4. Determine the mean of math proficiency scores of students taught by the New
Method.
Choices for 1 to 4
a) 69.4
b) 48.0
c) 74.0
d) 16.3
e) 70.9
f)
42.2
g) 29.3
h) 37.9
i) 77.0
j) 62.5
/continued
E
H
A
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STATISTICS 244.3
Term Test 1
5. Determine the Range of math proficiency scores of students taught by the New
Method.
6. Determine the Pseudo-Standard deviation (PSD) of math proficiency scores of
students taught by the New Method.
7. Determine the Range of math proficiency scores of students taught by the Standard
Method.
8. Determine the Interquartile Range (IQR) of math proficiency scores of students taught
by the New Method.
9. Determine the Pseudo-Standard deviation (PSD) of math proficiency scores of
students taught by the Standard Method.
10. Determine the standard deviation (s) of math proficiency scores of students taught by
the New Method.
11. Determine the Interquartile Range (IQR) of math proficiency scores of students
taught by the Standard Method.
12. Determine the standard deviation (s) of math proficiency scores of students taught by
the Standard Method.
Choices for 5 to 12
a) 50.2
b) 14.5
c) 66.80
d) 8.83
e) 9.80
f)
7.26
g) 29.26
h) 35.70
i) 22.31
j) 39.50
13. Find the Stem-leaf of math proficiency scores of students taught by the Standard
Method.
14. Find the Stem-leaf of math proficiency scores of students taught by the New Method.
Choices for 13 to 14
a) 0
b) 0
c) 0
d) 0
1
2
3
4
5
6
7
8
9
e)
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
6.2
3.4,4.5,5.1,7.1,9.2
1.1,3.9,4.6,6.0,6.3,7.6,7.7,7.8,8.3,9.0
0.9,1.1,8.6
3.6
f)
7.1,8.1,9.9
1.5,2.7,3.1,3.5,5.9,6.3
0.8,0.8,1.2,1.8,4.6,8.9,9.0
0.9,7.2,9.3
0.5
0
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
4.5
0.4,7.2
1.7,2.1,4.6,6.8,9.0
4.2,8.7,8.9,9.1
0.2,3.2,6.5
g)
0.0,9.3
3.8,6.3,6.7,8.8,9.5
1.0,2.0,3.4,6.4,6.8,6.8,7.0,7.8,8.7,8.8,8.9,9.3
2.0
0
1
2
3
4
5
6
7
8
9
3.3,3.4,4.2,4.7,7.8
1.8,1.9,2.5,3.4,7.3
7.1
1.3,7.7,8.2
9.9
-0.1
7.5
4.7
4.7,5.6
7.9,8.9
5.5
5.2,5.6,6.9,9.6
6.4
0.2,0.7
1
2
3
4
5
6
7
8
9
4.2,5.8
1.9,6.0,6.3,6.6,7.3,7.3,7.9,9.2,9.6
1.4,3.9,3.9,6.1,6.4,7.2
1.1,5.4,9.9
h) 0
1
2
3
4
5
6
7
8
9
0.7,3.8,4.5
3.7,6.6
3.4,6.9,7.9
2.0
5.2,5.6
3.2
0.3,1.6,7.5
C
G
H
J
F
I
E
D
D
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STATISTICS 244.3
II.
Term Test 1
Consider the data from two samples displayed in the two histograms:
Sample A
Sample B
30
30
25
25
20
20
f 15
f 15
10
10
5
5
0
0
10 to 20 20 to 30 30 to 40 40 to 50 50 to 60 60 to 70 70 to 80 80 to 90 90 to 100
10 to 20 20 to 30 30 to 40 40 to 50 50 to 60 60 to 70 70 to 80 80 to 90 90 to 100
Determine if the following statements are TRUE or FALSE.
15. The median for sample A is larger than the mean for sample A.
F
16. The mean for sample B is 65.
F
17. The Interquartile range (IQR) for sample B is at least 75.
F
18. The median for sample A is smaller than the median for sample B.
T
19. Sample A is a negatively skewed distribution.
F
20. For Normal distributions the mean and the median are approximately the same
T
The End
STATISTICS 244.3
Term Test 1