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AJ 503 Quantitative Methods Exercises

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AJ 503 Seminar in Quantitative Methods February 27, 2020
Spring 2020
Dr. Robert Mupier
ASSIGNMENT #2
(Due March 5, 2020)
1. Following are the numbers of days 30 juveniles in Harris County have spent on
probation.
(a) Find: - the mode - 84
- the median – 70+73 = 71.5
2
- the mean – 2116 = 70.53 = 71
30
(b) Provide an interpretation of each of these statistics
Mode: 84 is the most common number of days the 30 juveniles in Harris County
have spent on probation.
Median: 71.5 is the midpoint of the number of days the 30 juveniles in Harris
County have spent on probation.
Mean: 71 is the average of the number of days the 30 juveniles in Harris County
have spent on probation.
83 64 84 76 84 54 75 59 70 61
63 80 84 73 68 52 65 90 52 77
95 36 78 61 59 84 95 47 87 60
36 47 52 52 54 59 59 60 61 61
63 64 65 68 70 73 75 76 77 78
80 83 84 84 84 84 87 90 95 95
2. The number of days of absence from school for those juveniles in Harris County who
were on probation prior to their referral is given below.
(a) Group these data in five classes and find:
Grouping:
Group
Frequency
40-43
4
44-46
9
47-49
8
50-52
7
53-55
2
- the mode: 44
- the median: 47
- the mean: 1417/30 = 47.23

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52 47 50 47 44
54 46 46 45 46
53 41 50 44 44
49 47 43 48 51
49 40 50 51 43
51 46 44 48 48
(b) On the basis of the information obtained from (a) above, what can you
conclude about the shape of this distribution?
Sine mode < median < mean, we can conclude that the distribution is right
skewed
3. Using the sample data in exercise 2 above, find the variance and the standard
deviation of the ungrouped data. To do that:
a. Use the formula for the sample variance in Table 5.12 on page 121 of the
textbook by Bachman; look at the steps used to execute the formula in Table
5.13 on the same page.
X
X - µ
(X - µ)^2
52
4.77
22.72
54
6.77
45.79
53
5.77
33.25
49
1.77
3.12
49
1.77
3.12
51
3.77
14.19
47
-0.23
0.05
46
-1.23
1.52
41
-6.23
38.85
47
-0.23
0.05
40
-7.23
52.32
46
-1.23
1.52
50
2.77
7.65
46
-1.23
1.52
50
2.77
7.65
43
-4.23
17.92
50
2.77
7.65
44
-3.23
10.45
47
-0.23
0.05
45
-2.23
4.99
44
-3.23
10.45
48
0.77
0.59
51
3.77
14.19
48
0.77
0.59

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AJ 503 Seminar in Quantitative Methods Spring 2020 Dr. Robert Mupier ASSIGNMENT #2 (Due March 5, 2020) February 27, 2020 1. Following are the numbers of days 30 juveniles in Harris County have spent on probation. (a) Find: - the mode - 84 - the median – 70+73 = 71.5 2 - the mean – 2116 = 70.53 = 71 30 (b) Provide an interpretation of each of these statistics Mode: 84 is the most common number of days the 30 juveniles in Harris County have spent on probation. Median: 71.5 is the midpoint of the number of days the 30 juveniles in Harris County have spent on probation. Mean: 71 is the average of the number of days the 30 juveniles in Harris County have spent on probation. 83 63 95 36 63 80 64 80 36 47 64 83 84 84 78 52 65 84 76 73 61 52 68 84 84 68 59 54 70 84 54 52 84 59 73 84 75 65 95 59 75 87 59 90 47 60 76 90 70 52 87 61 77 95 61 77 60 61 78 95 2. The number of days of absence from school for those juveniles in Harris County who were on probation prior to their referral is given below. (a) Group these data in five classes and find: Grouping: Group 40-43 44-46 47-49 50-52 53-55 Frequency - the mode: 44 - the median: 47 - the mean: 1417/30 = 47.23 4 9 8 7 2 52 4 ...
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