FerrellJEDR8201-4

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Northcentral University *

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8201

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Statistics

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Jan 9, 2024

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FerrellJEDR8201-4 1 Examine the Normal Curve and Calculate Standard Scores Joyce E. Ferrell Department of Education, Northcentral University EDR-8201: Statistics I Dr. McKenna November 26, 2023

FerrellJEDR8201-4 2 Examine the Normal Curve and Calculate Standard Scores Table 2 Data from Four Science Assignments Studen t A1 A2 A3 A4 1 97 28 89 9 2 94 86 80 39 3 95 80 82 10 4 97 39 83 14 5 96 60 87 38 6 95 42 84 34 7 94 38 85 31 8 95 60 85 21 9 98 62 84 12 10 96 51 83 20 11 96 53 86 38 12 98 32 85 27 Part I:

FerrellJEDR8201-4 3

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FerrellJEDR8201-4 4 1. What scale of measurement do the data represent (i.e., nominal, ordinal, interval, ratio)? A variable has four different levels of measurement that it be classified as which are nominal, ordinal, interval, or ratio. Nominal is Latin for name only. It is only a name variable. The ordinal represents order or ranks. This means that one category may be better or bigger in status when compared to the others, and there is an order. Interval classifies like nominal and orders like ordinal and specifies the distance between intervals on the scales are equivalent. Ratio is very similar to that of interval except for the fact that ratio can have a value of 0 as well, and ratio allows 0 (Lloyd, 2021). The data represents the ratio level or the scale because 98 to 99 on the exam is the same interval up as 45 to 46 on an exam. You can still get a 0 option on the exam (Lloyd, 2021). 2. What is the mean and standard deviation for each assignment score? The mean for each of the assignments is as follows: A1: 95.92 A2: 52.58 A3: 84.42 A4: 24.42 The standard deviation for each of the assignments is as follows: A1: 1.379 A2: 18.108 A3: 2.353 A4: 11.532

FerrellJEDR8201-4 5 3. What is the median for each assignment score? A1: 96.00 A2: 52.00 A3: 84.50 A4: 24.00 4. What is the mode for each assignment score? A1: 95 A2: 60 A3: 85 A4: 38 5. What is the range for each assignment score? A1: 4 A2: 58 A3: 9 A4: 30 Part II: In a separate document (Word or Excel), create two columns to compare the totscores (total scores) and the tot tscores (total t-scores). Please use the following grade breakdown to rank the assignment grade scores 1 through 12, where 1 is the highest score A, and 12 the lowest score F: A to rank 1 B to rank 2 B– to rank 3 C+ to rank 4 C to ranks 5, 6, 7, and 8 C– to rank 9 D+ to rank 10 D to rank 11 F to rank 12

FerrellJEDR8201-4 6 Student totscores (total scores) tot tscores (total t-scores) 1 223.00 200.39 2 299.00 198.43 3 267.00 185.72 4 233.00 185.30 5 281.00 227.46 6 255.00 194.05 7 248.00 186.23 8 261.00 196.96 9 256.00 207.77 10 250.00 189.88 11 273.00 219.34 12 242.00 208.46 Student totscores (total scores) Rankin g Grade tot tscores (total t-scores) Rankin g Grade 1 223.00 12 F 200.39 5 C 2 299.00 1 A 198.43 6 C 3 267.00 4 C+ 185.72 11 D 4 233.00 11 D 185.30 12 F 5 281.00 2 B 227.46 1 A 6 255.00 7 C 194.05 8 C 7 248.00 9 C- 186.23 10 D+ 8 261.00 5 C 196.96 7 C 9 256.00 6 C 207.77 4 C+ 10 250.00 8 C 189.88 9 C- 11 273.00 3 B- 219.34 2 B 12 242.00 10 D+ 208.46 3 B- 6. Determine what is unusual about student 1’s performance on the tests. What is unusual about student 1’s performance is that on assignments 1 and 3, the student performed well, but on assignments 2 and 4, the student had low scores. This is unusual since the student obtained a ranking of 5 for total t-scores compared to a ranking of 12 for the total scores. 7. What is strange about student 2’s performances? How do the performances of these two students differ, and how are they the same?

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FerrellJEDR8201-4 7 The strange thing about student 2, as compared to student 1, student 2 performed well on tests 1,2 and 3. Based on the performance of students 1 and 2, student 1 had a low average going into test 4, and student 2 had a higher average going into test 4. On test 4, both students received a failing grade. 8. What grades would be assigned to these two students if the total of the raw scores were used to determine grades? If the raw scores were to be used, student 2 would have an A, and student 1 would be assigned an F. 9. What grades would be assigned to these two students if the total of the t-scores were used to determine grades? If the total of the t-scores were used, both students would have received a C grade. 10. Why are your answers to questions 9 and 10 different? (hint: examine the variability of the tests) My answers to questions 9 and 10 differ because of their scores and variabilities. Assignments 1 and 3 had low variability in scores (a range of 4 and 9), while assignments 2 and 4 had high variability in scores (a range of 58 and 30). When looking at the scores of student 1, it is visible that they scored high on assignments 1 and 3 but low on assignments 2 and 4. This is the opposite of what student 2 scored. Student 2 scored higher on assignments 1 and 2 and lower on 3 and 4. 11. What are the means and the standard deviations of the four z-score distributions (to one decimal point)?

FerrellJEDR8201-4 8 When using this table as a reference, the mean is 0, and the standard deviation is 1.0. 12. What are the means and standard deviations of the four t-score distributions (to one decimal point)? When using this table as a reference, the mean is 50.0, and the standard deviation is 10.0.

FerrellJEDR8201-4 9 References Lloyd, C. (2021, July 6). Stats I Week 4 Assignment Part 1 of 2 [Video]. Kaltura.

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