Answered step-by-stepCase Study 5: Descriptive Statistics about Bicycle Commuting Use...
Case Study 5: Descriptive Statistics about Bicycle Commuting
Use Item 1: Number of People Who Bike to Work in Select States (given on the last page of this document) to answer the following questions and prompts.
- Use your calculator to calculate the following measures of central tendency for this data set (1/2 point each).
a. Mean (round to the tenths place):
b. Median:
2. Which measure of central tendency (above) is more representative of this data set? Explain (2 points).
3. Use your calculator to calculate the 5-number summary for this data set (1/2 point each).
a. Minimum:
b. Lower quartile (Q1):
c. Median (from question 1):
d. Upper quartile (Q3):
e. Maximum:
4. Calculate the following measures of variability for this data set (1/2 point each).
a. Range (lowest to highest):
b. Interquartile range (IQR = Q3 minus Q1):
5. Which measure of variability (above) provides a better description of this data set? Explain (2 points).
6. make a box plot in the space below to represent the data set, making sure to label all its components (6 points). If you want to create one electronically, you can use this website: http://www.alcula.com/calculators/statistics/box-plot/ Enter the 10 values in the box separated by commas, then hit "submit data". You need to save the image to your device and then paste it here. It will not let you copy/paste directly (usually).
7. Assess the potential impact of an outlier in the data set by answering the questions and prompts below.
- By just looking at Item 1: Number of People Who Bike to Work in Select States (given on the last page of this document), which state do you think might represent an outlier in this data set (1 point)?
- For a value to be considered an outlier, it must be greater than (1.5*IQR) + Q3 or less than Q1 - (1.5*IQR). Use math to verify whether the state you identified above qualifies as an outlier for this data set (1/2 point).
- Describe the impact of this outlier on the mean, median, and shape of the data distribution. In other words, how do these values change (if at all) when the outlier is left in or taken out (1 point)?
- Why do you think the number of people who bike to work in the outlier state differs noticeably from that of the other states (1 point)?
- List additional states not included in Item 1 that you suspect might also be high outliers in terms of the number of people who bike to work. Explain why you listed each state as a potential high outlier (1 point).
- Which of all the U.S. states would you predict has the greatest number of people who commute by bicycle. Why (2 points)?
- Based on the mathematical definition of an outlier, is it possible that a state not listed in Item 1 is a low outlier with respect to the number of people who bike to work? Explain your reasoning (2 points).
8. Assess the potential utility of outliers by answering the questions and prompts below.
- How does the presence of an outlier in this particular data set help bring attention to significant factors (i.e., "lurking variables") that might influence the number of people who bike to work in a state? List one or two possible factors (i.e., "lurking variables") (2 points).
- Do you think any of these significant factors could be identified if the outlier were not present? Explain your reasoning. In other words, if there was no outlier in the data, would we even think about these factors (1 point)?
- Thinking beyond this data set, what general role might outliers play in developing an understanding of data sets (1 point)?
9. Are the states included in this data set the appropriate states to compare? Explain your reasoning (2 points).
10. Thinking about how the number of bike commuters was calculated in this data set, what impact might the sheer population of a state have on the number of its residents who bike to work? In other words, how might the number of people living in a state (its population) be related to the number who bike to work (2 points)?
11. How else could the number of people who bike to work be calculated to account for the impact of state population (think back to Chapter 9 for this response) (2 points)?
Item 1: Number of People Who Bike to Work in Select States
| State | Number of bicycle commuters |
|---|---|
| Alabama | 2,505 |
| Alaska | 3,553 |
| Connecticut | 5.320 |
| Delaware | 1,329 |
| Florida | 54,652 |
| Georgia | 9,735 |
| Idaho | 6,746 |
| Kansas | 4,814 |
| Maryland | 8,955 |
| Virginia | 15,564 |
Source for data: U.S. Census Bureau, Means of Transportation to Work. 2011-2013 American Community Survey 3-Year Estimates.
Answer & Explanation
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