A researcher from the ministry of education wants to find out if there is an academic difference in students from different parishes in Jamaica based on the CSEC examinations. He selected 20 students who completed the exam from three parishes; St James, St Ann, Kingston. He will assess them based on their English and Mathematics scores. Use the provided data to do the following questions. See the tablw below t answer Questions ID Parish English Mathematics 1 StJames 90 92 2 StJames 83 83 3 StJames 80 70 4 StJames 82 65 5 StJames 90 92 6 StJames 95 94 7 StJames 98 66 8 StJames 96 77 9 StJames 81 78 10 StJames 84 80 11 StJames 63 70 12 StJames 71 66 13 StJames 72 68 14 StJames 66 69 15 StJames 75 75 16 Kingston 79 74 17 kingston 67 63 18 kingston 65 62 19 kingston 65 77 20 kingston 60 67 21 kingston 64 75 22 kingston 68 82 23 kingston 69 66 24 kingston 77 77 25 kingston 56 60 26 kingston 59 78 27 kingston 57 55 28 kingston 60 68 29 kingston 52 67 30 kingston 50 53 31 StAnn 55 57 32 StAnn 56 70 33 StAnn 57 60 34 StAnn 67 72 35 StAnn 59 60 36 StAnn 58 57 37 StAnn 53 65 38 StAnn 54 54 39 StAnn 60 62 40 StAnn 51 52 41 StAnn 56 57 42 StAnn 57 30 43 StAnn 58 59 44 StAnn 52 54 45 StAnn 57 58 1. Classify the variables and the measurement scale used. 2. Discuss the sampling method you would use to select the 20 students. List two limitations of the method selected. 3. Discuss two (2) possible types of errors that may arise in this research. 4. Calculate an appropriate measure of central tendency for each of the variables in the data set and explain your choice for each variable. 5. Generate appropriate graphs for the parishes, and the subjects and explain your choice for each. 6. Do you think that the mean score for each subject is a good measure of central tendency to confirm which parish did the best in CSEC? Explain. 7.Compute and explain skewness for the grades using Pearson's 1 st measure of skewness. 8. How could knowledge of probabilities be used to analyse the data given in the table? 9. Manipulate the data given to calculate any two probabilities. 10. All other things being constant, which of the three parishes would you recommend to someone who wants to guarantee that their child does well in CSEC? Give one reason. *You response should be based on the data and the calculations you have done. 11. Search for data on the CSEC passes for students from any two of the three parishes and for any given year. Which of the two parishes did the best in the year selected?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A researcher from the ministry of education wants to find out if there is an academic difference in students from different parishes in Jamaica based on the CSEC examinations. He selected 20 students who completed the exam from three parishes; St James, St Ann, Kingston. He will assess them based on their English and Mathematics scores. Use the provided data to do the following questions.
See the tablw below t answer Questions
|
ID |
Parish |
English |
Mathematics |
|
1 |
StJames |
90 |
92 |
|
2 |
StJames |
83 |
83 |
|
3 |
StJames |
80 |
70 |
|
4 |
StJames |
82 |
65 |
|
5 |
StJames |
90 |
92 |
|
6 |
StJames |
95 |
94 |
|
7 |
StJames |
98 |
66 |
|
8 |
StJames |
96 |
77 |
|
9 |
StJames |
81 |
78 |
|
10 |
StJames |
84 |
80 |
|
11 |
StJames |
63 |
70 |
|
12 |
StJames |
71 |
66 |
|
13 |
StJames |
72 |
68 |
|
14 |
StJames |
66 |
69 |
|
15 |
StJames |
75 |
75 |
|
16 |
Kingston |
79 |
74 |
|
17 |
kingston |
67 |
63 |
|
18 |
kingston |
65 |
62 |
|
19 |
kingston |
65 |
77 |
|
20 |
kingston |
60 |
67 |
|
21 |
kingston |
64 |
75 |
|
22 |
kingston |
68 |
82 |
|
23 |
kingston |
69 |
66 |
|
24 |
kingston |
77 |
77 |
|
25 |
kingston |
56 |
60 |
|
26 |
kingston |
59 |
78 |
|
27 |
kingston |
57 |
55 |
|
28 |
kingston |
60 |
68 |
|
29 |
kingston |
52 |
67 |
|
30 |
kingston |
50 |
53 |
|
31 |
StAnn |
55 |
57 |
|
32 |
StAnn |
56 |
70 |
|
33 |
StAnn |
57 |
60 |
|
34 |
StAnn |
67 |
72 |
|
35 |
StAnn |
59 |
60 |
|
36 |
StAnn |
58 |
57 |
|
37 |
StAnn |
53 |
65 |
|
38 |
StAnn |
54 |
54 |
|
39 |
StAnn |
60 |
62 |
|
40 |
StAnn |
51 |
52 |
|
41 |
StAnn |
56 |
57 |
|
42 |
StAnn |
57 |
30 |
|
43 |
StAnn |
58 |
59 |
|
44 |
StAnn |
52 |
54 |
|
45 |
StAnn |
57 |
58 |
1. Classify the variables and the measurement scale used.
2. Discuss the sampling method you would use to select the 20 students.
List two limitations of the method selected.
3. Discuss two (2) possible types of errors that may arise in this research.
4. Calculate an appropriate measure of
5. Generate appropriate graphs for the parishes, and the subjects and explain your choice for each.
6. Do you think that the mean score for each subject is a good measure of central tendency to confirm which parish did the best in CSEC? Explain.
7.Compute and explain skewness for the grades using Pearson's 1 st measure of skewness.
8. How could knowledge of probabilities be used to analyse the data given in the table?
9. Manipulate the data given to calculate any two probabilities.
10. All other things being constant, which of the three parishes would you recommend to someone who wants to guarantee that their child does well in CSEC? Give one reason.
*You response should be based on the data and the calculations you have done.
11. Search for data on the CSEC passes for students from any two of the three parishes and for any given year. Which of the two parishes did the best in the year selected?
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