The professor knows that there are a maximum of 100 points for each of the three unit exams and a maximum of 200 points for the final exam. Based on the college's grading scale, the final grade in this course will be determined by the following total point value ranges.
Table: Prescott College Uniform Grading Scheme for General Biology Classes
Final Grade
Percentiles Minimum points Maximum points
A 94 to 100 470 500
A- 89 to 93 445 469
B+ 85 to 88 425 444
B 82 to 84 410 424
B- 78 to 81 390 409
C+ 74 to 77 370 389
C 70 to 73 350 369
C- 66 to 69 330 349
D+ 61 to 65 305 329
D 57 to 60 285 304
D- 52 to 56 260 284
F 51 and below 0 259
As an example, if student A earns 75, 87, and 90 points on the three unit exams and an additional 168 points on the final exam, their total points would be 420 points and they would earn a B in the class (their total fell into the range of 410 to 424 or the B range from this table above).
Your Tasks:
You will help professor McPherson by doing the following tasks and analyzing the results for each task .
1. Complete a one variable summary for all 25 students over the three unit exams and the final exam.
a. What do these statistics tell you about the group of students? Be specific and look at the range, standard deviation, the IQR, the mean versus the median and other statistics from this output.
2. Complete a single histogram on all four of these test scored and analyze the results.
a. What do these histograms tell you about the overall grades for each of these exams?
3. Complete 4 Q-Q plots for these exams.
a. What do these plots tell you about the data? Is it relatively normal or not and why?
4. Complete a single box and whisker plot with all four of the exams on it.
a. First explain what a box and whisker plot is, and how to understand it.
b. What do these box and whisker plots tell you about the individual exams and how do they compare to each other?
5. Complete a multiple regression using the final exam as the dependent variable, and the unit exams as the independent variables.
a. Do any of the variables exceed the alpha for this test? If so, remove that/those variables and rerun the regression.
b. What does the r-squared value tell you about this data?
c. What does the standard error of the estimate tell you about the data?
d. According to the f-ratio, is this regression significant or not and why?
e. Using the coefficients generate predict the final exam points, the final course total points and the final grade for the five "typical" students found in Table 1 above. (You are to complete the three columns found on the right in yellow and include this table in your mini report.)
6. What general things can you tell professor McPherson about the types of students who will either earn a good grades (B to A) or a poor grades (F to D) based on the first three unit exams? Be specific. (Yes, you should be able to figure this out, look at the results for both the original data and for the 5 students, that will tell you how to determine who might make good or poor grades.)