Illinois State University Mathematics Department
MAT 312: Probability and Statistics for Middle School Teachers
Problem Set #2
look at possible solutions
A. For the first question, you are to create a specified data set and then represent it in various ways.
Create a season record of 20 game-point totals for one womens' basketball team (i.e., twenty numbers like 56, from the score ISU 56, Bradley 53). Create the data set to meet all of the following characteristics:
- The mean score is between 70 to 73 points.
- The median score is at least 6 points higher than the mean score.
- The population standard deviation is less than 12 points.
- The scores range from the 55 to the 86, inclusive.
- There are at least 15 different scores.
To represent your data set:
1. List the scores in ascending order.
2. Create a stem-and-leaf plot and a box-and-whiskers plot of your data set.
3. List the mean, the median, the range, the population standard deviation, the 5-number summary, and the upper and lower inner and outer fences.
Finally, respond to these questions, with respect to your data set:
4. Describe the data as either nominal, ordinal, interval, or ratio data. Justify your choice.
5. Based on your data set, comment on whether or not this womens' team had a winning or losing basketball season.
B. Here are some prices of compact-disc players from Consumer Reports. Generate a description of the prices for this set of CD players. Your description should include written, numerical, and visual representations.
6. In your description, clearly identify the location, spread, and shape of the data.
7. Examine and reflect upon the representations you chose to use in your description. Why did you choose those particular representations?
C. Here are statistics for the top 50 finishers in the 1994 Iditarod Dog Sled Race. The information was transferred from a file found on the Internet. Use the data to respond to the following questions.
8. Create a box plot and an absolute frequency histogram of the elapsed race times for the top 50 finishers. Note that race-time information is given in the four columns on the right side of the table, where elapsed time is expressed in days, hours, minutes, and seconds.a. On your box plot, label the 5-number summary of the data.
b. State the inner and outer fences as units of time expressed in parts of a day to the nearest hundredth of a day (e.g., 12.54 days). Show the four fences on your box plot.
c. Your box plot should be the type of box plot that identifies outliers with solid and hollow dots, if any exist.
d. Line up vertically your box plot and your histogram so they share the same horizontal scale. Comment on similarities and differences in what is revealed in these two visual summaries.
9. Use your calculator to create a scatter plot to compare the number of dogs on a team (fifth column in from right edge of table) to the elapsed race time for that team. Use the horizontal axis for number of dogs and the vertical axis for elapsed race time. Express elapsed race time in parts of a day as explained in question 8(b).
Write a brief, specific, and justifiable statement to describe what is revealed in the scatter plot about the relationship between the number of dogs on a team to the elapsed race time for that team. (You DO NOT need to sketch your scatter plot.)
10. Use your calculator to generate a median-median line of best fit to model the relationship between the number of dogs on a team and the elapsed race time, expressed in parts of a day, for that team.a. Write the equation of the median-median line. Use d as the independent variable that represents the number of dogs and t as the dependent variable that represents the elapsed race time for a team. In your equation, round the slope and the t&endash;axis intercept to the nearest thousandth of a unit.
b. According to the median-median line, what race time is predicted for a team of 13 dogs? How does that compare to actual race results?
c. Identify the three ordered pairs that represent the centers of each one third of the data set, according to the median-median line procedure
11. What information in the data table can be used to conclude that more than 50 racers participated? Explain.
Assigned: Tuesday 16 February 1999
Due: Tuesday 23 February 1999