14A Coreq

In the next in-class activity, you will need to visually assess and make comparisons  between groups using graphical displays. This corequisite support activity will provide a  review of interpreting graphical displays and making connections between graphs,  measures of variation, and measures of center.

Interpreting Graphical Displays

This support activity revisits data from a sleep study[1] that we’ve explored throughout the  course. Recall that the researchers in this study were interested in a number of  variables related to college students’ sleeping habits, health, academic success, and  alcohol consumption.

Question 1

1) The following boxplots summarize the number of morning classes missed by  students based on whether they consumed a large number of alcoholic drinks per  week (Heavy), a moderate number of alcoholic drinks per week (Moderate), a few  alcoholic drinks per week (Light), or no alcoholic drinks per week (Abstain).Side-by-side box plots labeled “Classes Missed” on the horizontal axis, with “Heavy,” “Moderate,” “Light,” and “Abstain” on the vertical axis. For heavy, the low point is at approximately 0 and the high point is approximately 6, with the low end of the box at approximately 0.5, the high end at approximately 3, and the middle line at approximately 2. For moderate, the low point is at approximately 0 and the high point is at approximately 10. The low end of the box is at approximately 0, the high end is at approximately 4, and the middle line is at approximately 2. There are also points at approximately 13, 14, 15, and 20. For light, the low point is at approximately 0 and the high point is at approximately 5. The low end of the box is at approximately 0, the high end is at approximately 2, and the middle line is at approximately 1. There are also points at approximately 6, 7, 10, and 12. For Abstain, the low point is at approximately 0 and the high point is at approximately 2. The low end of the box is at approximately 0, the high end of the box is at approximately 1, and no middle line can be identified. There are also points at approximately 4, 14, 15, and 20.

Part A: Compare and contrast the classes missed between the groups. Is there  anything in particular that you notice from the boxplot?

Part B: Compare the medians from each group. Which group(s) appear(s) to have the greatest median number of classes missed?

Part C: Based on the boxplots, which group appears to have less variation in the  number of classes missed—the Heavy group or the Moderate group? How  do you know?

Question 2

2) The following boxplots and histograms (continued on the next page) illustrate the  number of morning classes missed by students based on whether they identified as  Morning Larks, Night Owls, or Neither.

Side-by-side box plots labeled “Missed Classes” on the x-axis, with “Lark,” “Owl,” and “Neither” on the y-axis. For Lark, the low point is at 0 and the high point is at approximately 5. The low end of the box is at 0, the high end is at approximately 2, and the middle line is at approximately 1. There are also points at approximately 6 and 8. For Owl, the low point is at 0 and the high point is at approximately 12. The low end of the box plot is at approximately 1, the high end is at approximately 5, and the middle line is at approximately 2. There are also points at approximately 13, 14, 15, and 20. For neither, the low point is at 0 and the high point is at 5. The low end of the box is at 0, the high end is at 2, and the middle line is at 1. There are also points at approximately 6, 7, 10, and 14.Side-by-side histograms labeled “Missed Classes” on the x-axis. There is a legend showing that green indicates lark, yellow indicates owl, and brown indicates neither. The first histogram is green. For 0, the value is approximately 17. For 1-2, the value is approximately 8. For 3, the value is approximately 2. For 4, the value is approximately 1. For 5-6, the value is approximately 2. For 8, the value is approximately 1. The next histogram is yellow. For 0-4, the value is approximately 35. For 5-9, the value is approximately 7. For 10-14, the value is approximately 5. For 15-20, the value is approximately 3. The next histogram is brown. For 0, the value is approximately 65. For 1, the value is approximately 35. For 2, the value is approximately 24. For 3, the value is approximately 11. For 4, the value is approximately 8. For 5-6, the value is approximately 7. For 10, the value is approximately 2. For 14, the value is approximately 1.

Part A: Compare and contrast the classes missed between the various groups. Is  there anything in particular that you notice from the boxplot and histogram?

Part B: Based on the previous graphical displays, if we were to calculate the  standard deviation for each of these groups, which group do you think would  have the greatest value? Explain.

Part C: Based on the previous graphical displays, if we were to calculate the median for each of these groups, which group would have the greatest value?  Explain.

Part D: Based on the previous graphical displays, if we were to calculate the mean for each of these groups, which group do you think would have the greatest value? Explain.

Question 3

3) Using the DCMP Describing and Exploring Quantitative Variables tool at  https://dcmathpathways.shinyapps.io/EDA_quantitative/, select the appropriate dataset and calculate descriptive statistics for the classes missed based on whether  individuals identified as Morning Larks, Night Owls, or Neither. Complete the following table.

Sleep Type n Mean Median Std. Dev.
Morning Lark
Night Owl
Neither

Question 4

4) Do your calculations align with your answers in Question 2? Explain.

  1. Onyper, S. V., Thacher, P. V., Gilbert, J. W., & Gradess, S. G. (2012). Class start times, sleep, and  academic performance in college: A path analysis. Chronobiology International, 29(3), 318–335. ↵