Height vs



Height vs. Shoe size P-BIT

Algebra 2

We’ve just found out that a shoe retailer is considering opening a discount shoe store downtown on the Harlan Square. This store offers many different brand name shoes at discounts of 40 to 60 percent. It can do this because it buys in “bulk” and keeps a rather restricted inventory to cut overhead costs. This store has asked that we help collect data since their target audience is to be students of high school age. Based on our research, they need us to give them a recommendation as to how many shoes and of what sizes they need to have in stock.

The shoe retailer’s research department has found that there is a high correlation between a person’s height in inches and their shoe size, so we will be collecting data on both measurements. From there, you will be asked to find a regression equation showing the relationship between height and shoe size.

Tasks:

1. Collect data from the class to assist in the process of “limiting” the inventory needed to be successful. Gather each student’s height (to the nearest ½ inch) and shoe size (to the nearest half size). To make the data uniform, subtract 1.5 from girls’ shoe size. For example, if a girl has a shoe size of 7, record their size as 5.5 (7 – 1.5 = 5.5).

2. Use this data to make a hand-made scatter plot (you may also turn in a computer-generated scatter plot if you wish)

a. Consider carefully which measurement will be your independent variable and which will be your dependent variable.

b. Also consider what scale you will use for each axis and state the reason you decided what you did.

3. Draw a line of best fit on your data and hand calculate the equation of that line.

4. Then use a graphic calculator or excel spreadsheet to generate another regression equation.

What is that equation?

5. Try your equation for best fit line on one girl and one boy. Have them give you their height. Does your formula accurately predict their shoe size? Why or why not? Show your calculations. What girls’ size would your female need?

6. What is the range of your shoe sizes? Calculate the upper and lower outlier limits. Are there any outliers? What would you do if you had one? Why? Are the outliers, if they exist, important to your findings? Why or why not?

7. Find the mode, median, and mean of the shoe sizes. Then, explain which measure of central tendency would be best for the store owner to use when determining inventory. It would also be good to explain why you should not use the other two measures of central tendency.

8. The store would like to carry an inventory that would meet the needs of about 80% of the class population. What shoe sizes and how many of each would you ask them to keep on hand based on your research? How can you justify this to the store owner?

9. If the store is going to stock shoes for 80% of a teenage population of 1000 customers, state specifically how many of each shoe size they should carry and show the math to justify.

10.)What are some conditions that might make this experiment’s results questionable? What could you do to alleviate some of these concerns?

Height vs. Shoe size P-BIT Total points: __________/ 30

Score sheet

1. Scatter plot, line of best fit, and equation (10 points):

a. Was scatter plot drawn accurately?

b. Was everything labeled?

c. Was the correct variable used for the independent variable?

d. Was line of best fit drawn accurately?

e. Was prediction equation computed correctly?

2. Range and outliers (5 points):

a. Was range and outlier limits computed accurately?

b. Explanation of importance of outliers?

3. Mean, median, and mode (5 points)

a. Were the three computed correctly?

b. Explanation of which one is best for this situation?

4. Prediction equation test (5 points)

a. Was one boy and one girl tested?

b. Was work shown?

c. Explanation of whether or not shoe sizes matched up?

d. Was girl’s size accurately calculated?

5. Recommendation to store owner to cover 80%. (5 points)

a. Was 80% of the data accurately found?

b. Was the recommendation clearly stated?

c. Was the recommendation justified?

d. Was recommendation for population of 1000 correct?

e. Were at least two reasons given for what was wrong with our sample?

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