Curving the Test
By: Katy Benesch, Rachel Draplin, and Lauren Toma
1) Is curving the test appropriate in the following situations? Explain.
a. A fire drill occurs while students are taking a test. They lose 15 minutes of the period and only one student has finished the test at the end of the class.
Yes, because every student deserves the equal amount of time to complete his or her test. If students in other periods got the full class to take it, so should the period which had the fire drill.
b. On a multiple choice test, the teacher inadvertently leaves out the correct answer for one problem.
Yes, because if the correct answer was left out, then there is no way any of the students could've gotten the answer correct. It would be completely unfair for a student's grade to be lowered if they knew the right answer.
c. On a chapter test, no student scores an A.
Yes or no, depending on the circumstance. If the teacher put material on the test that was never covered in class, if they provided little to no help prior to the test, or if it was the fault of the teacher for any other reason, then yes, it would be appropriate to curve it. On the other hand, if the students were offered a good amount of review and information, but simply failed to study it, then a curve wouldn't be necessary.
d. On a chapter test, all students score an A.
No, because the students all benefit from the good grade and the teacher receives a high average. It is clear that the students have been well prepared for the test, and therefore there is no reason to lower or raise any scores.
e. On a chapter test, the teacher expected the average score to be an 80% but was surprised that it was 73% instead.
Yes or no. Perhaps the teacher had well prepared his or her students, and it was them who failed to study accordingly. Or, it could be possible that the teacher over-estimated the knowledge that the students knew, and therefore didn't provide a sufficient amount of study material before the test.
f. A problem on the test was poorly worded, making it more difficult to solve.
Yes, because the teacher had the opportunity to warn them about that specific question and provide further explanation for it, but didn't.
2) What are the benefits to curving a test? What are some possible drawbacks?
The benefits are that everyone receives a better score and the the test average goes up, also benefiting the teacher. A possible drawback would be that the people who put a lot of effort into studying did not get their deserved recognition.
3) Explain what it means for test scores to be normally distributed about a C average. Do you agree or disagree that a good test has a normal distribution about a C average? Explain.
For a test to be distributed at a C average, there must be a balanced amount of high and low scores. If a test is normally distributed, the majority of scores will fall in the C range,
4) Use the table.
Class Scores for Chapter 11 Test
73 68 70 67 70 92 72 92 75 83 74 75 83
72 98 81 79 89 96 88 75 95 89 79 97 96
a. Make a histogram of the chapter 11 test data in the table and calculate the mean, the median, the mode, the range, and the standard deviation for those scores.
Mean: 81.84
Median: 80
Mode: 75
Range: 31
Standard Deviation: 9.57
b. Is this data normally distributed? Why or why not?
No, it is not normally distributed. The histogram is skewed right, and is not symmetrical.
5) One curving technique adds a constant number of points to each score. This is sometimes called a grade bump or a flat curve. It can be applied to change the highest or median grade to a certain value or to make up for an unfair or difficult problem.
a. Apply a flat curve to the initial test score data so that the highest score is 100. Record the curved scores.
75 70 72 69 72 94 74 94 77 85 76 77 85
74 100 83 81 91 96 90 77 97 91 81 99 98
b. Make a histogram of the curved data and calculate the mean, the median, the mode, the range, and the standard deviation for the data set.
a. A fire drill occurs while students are taking a test. They lose 15 minutes of the period and only one student has finished the test at the end of the class.
Yes, because every student deserves the equal amount of time to complete his or her test. If students in other periods got the full class to take it, so should the period which had the fire drill.
b. On a multiple choice test, the teacher inadvertently leaves out the correct answer for one problem.
Yes, because if the correct answer was left out, then there is no way any of the students could've gotten the answer correct. It would be completely unfair for a student's grade to be lowered if they knew the right answer.
c. On a chapter test, no student scores an A.
Yes or no, depending on the circumstance. If the teacher put material on the test that was never covered in class, if they provided little to no help prior to the test, or if it was the fault of the teacher for any other reason, then yes, it would be appropriate to curve it. On the other hand, if the students were offered a good amount of review and information, but simply failed to study it, then a curve wouldn't be necessary.
d. On a chapter test, all students score an A.
No, because the students all benefit from the good grade and the teacher receives a high average. It is clear that the students have been well prepared for the test, and therefore there is no reason to lower or raise any scores.
e. On a chapter test, the teacher expected the average score to be an 80% but was surprised that it was 73% instead.
Yes or no. Perhaps the teacher had well prepared his or her students, and it was them who failed to study accordingly. Or, it could be possible that the teacher over-estimated the knowledge that the students knew, and therefore didn't provide a sufficient amount of study material before the test.
f. A problem on the test was poorly worded, making it more difficult to solve.
Yes, because the teacher had the opportunity to warn them about that specific question and provide further explanation for it, but didn't.
2) What are the benefits to curving a test? What are some possible drawbacks?
The benefits are that everyone receives a better score and the the test average goes up, also benefiting the teacher. A possible drawback would be that the people who put a lot of effort into studying did not get their deserved recognition.
3) Explain what it means for test scores to be normally distributed about a C average. Do you agree or disagree that a good test has a normal distribution about a C average? Explain.
For a test to be distributed at a C average, there must be a balanced amount of high and low scores. If a test is normally distributed, the majority of scores will fall in the C range,
4) Use the table.
Class Scores for Chapter 11 Test
73 68 70 67 70 92 72 92 75 83 74 75 83
72 98 81 79 89 96 88 75 95 89 79 97 96
a. Make a histogram of the chapter 11 test data in the table and calculate the mean, the median, the mode, the range, and the standard deviation for those scores.
Mean: 81.84
Median: 80
Mode: 75
Range: 31
Standard Deviation: 9.57
b. Is this data normally distributed? Why or why not?
No, it is not normally distributed. The histogram is skewed right, and is not symmetrical.
5) One curving technique adds a constant number of points to each score. This is sometimes called a grade bump or a flat curve. It can be applied to change the highest or median grade to a certain value or to make up for an unfair or difficult problem.
a. Apply a flat curve to the initial test score data so that the highest score is 100. Record the curved scores.
75 70 72 69 72 94 74 94 77 85 76 77 85
74 100 83 81 91 96 90 77 97 91 81 99 98
b. Make a histogram of the curved data and calculate the mean, the median, the mode, the range, and the standard deviation for the data set.
Mean: 83.85
Median: 84
Mode: 77
Range: 31
Standard Deviation: 10.19
c. Is this data normally distributed? Why or why not?
No, the histogram isn't symmetrical, therefore it is not normally distributed.
d. What statistics changed from the original data set? Which ones remained the same? Why?
All of the statistics increased slightly, except for the range, which stayed the same.
Median: 84
Mode: 77
Range: 31
Standard Deviation: 10.19
c. Is this data normally distributed? Why or why not?
No, the histogram isn't symmetrical, therefore it is not normally distributed.
d. What statistics changed from the original data set? Which ones remained the same? Why?
All of the statistics increased slightly, except for the range, which stayed the same.