1. Chapter 2
Center and Variation

2. 1. A class of 25 students was polled and asked how many credit hours they were attempting in fall The responses were:
Find the mean, median, and mode(s) of this data, and make a frequency table of the data.

3. 2. Each semester on the student evaluations, students are asked to rate their own performance in the course. One semester, 1122 students answered this question on an evaluation in the Department of Mathematics at AU. Here are the results.
Weight the data by frequency, and determine the mean and median student "self-rating".
(Note: If you said “is this data really at the interval level”, you would be correct to do so.)

4. 3. Suppose a class of 12 students took an exam. The scores were:
Find the mean score on the exam. Then, remove the exam score that is an obvious outlier*, and redo the calculation.
*-not always a good idea; sometimes outliers tell you things!

5. 7. See problems 1,2, and 3. Find the sample standard deviation of the quantity of interest in each problem.

6. 8. The mean score on the SAT-M exam is usually around 500 with a standard deviation of 100, and the mean on the ACT-M exam is usually around 19 with a standard deviation of about 4 points.
a. Someone looks at this information, sees that the standard deviation on the SAT is higher, and concludes that there is much more variation in scores on the SAT test. Explain why this statement is patently ridiculous.
b. Two students are in the running for a scholarship, and their SAT/ACT score will be the deciding factor. Student A scored 720 on the SAT, while student B scored 29 on the ACT. Who’s the winner?

7. 9. Dr. Smith gives a calculus exam where the mean score is 74 and the (population) standard deviation is 7.5. Use Chebyshev’s Theorem to find an interval containing at least 88.9% of the exam scores.

8. 10. Dr. Smith once gave a college algebra exam where the mean score was 53 and the standard deviation was 28 (true story!). Use Chebyshev’s Theorem to find an interval containing at least 75% of the exam scores.