Assignment #8: Descriptive Statistics

Assignment #8

1.      The students in two fourth grade classes were clocked for the time (to the nearest second) required to run completely around the school’s playground. The results are as follows:

            Times for Mr. Robertson’s class:        56, 48, 61, 67, 72, 59, 74, 58, 47

                                                                        57, 53, 48, 45, 62, 50, 53, 51, 72

            Times for Ms. Grants’ class:               65, 63, 78, 49, 58, 71, 56, 53, 78

                                                                        67, 79, 45, 55, 54, 62, 54, 61

a.   Construct a stem and leaf display with a central stem with Mr. Robertson’s class on the left and Ms. Grants’ class on the right. Order the leaves with the smallest leaves closest to the stem.

b.   Which class had the better performance? Explain by referring to the stem and leaf plot.

2.      In a survey of my current Math classes (total of 40 students), the following data was collected: 12 students are in choir, 10 are involved in athletics, 5 are either RA’s or Chaplains, 8 are in Concordia Teacher Corp, and 5 have other commitments off campus.

a.   Draw a bar graph displaying this data.

b.   Draw a pie chart for this data. (Show the size of each central angle to the nearest degree.)

3.      The Portland School district administered two year-end mathematics achievements tests to its fifth graders. The state test had a mean of 197 and a standard deviation of 13.2. The national test had a mean of 39 and a standard deviation of 2.9. (Compute the z-scores to the nearest hundredth.)

a.   What is the z-score for a state score of 226?

b.   What is the z-score for a national score of 45?

c.   Which of the two test scores from parts a and b indicates the stronger performance? Explain.

4.      Given the following results on the GRE (Graduate Record Exam) where the top row of numbers listed for each subject test shows the raw score for that subtest. The number in the second row of each column shows the national percentile.

a.   Nationally, what percentage of the students scored below this student in Verbal Skills? 

b.   What percentage of the students scored above this student in Mathematics?