Course 1 Unit 1

Lesson 2 Investigation 3-Measures of Center

Page 31

1. Prepare a back-to-back stem-leaf plot of the cholesterol in the burger and chicken entrees.

a. Copy the stems shown at the right. Put the leaves for the chicken entrees to the right of the stems and put the leaves for the burgers to the left of the stems.


  1. In general, is there more cholesterol in a burger or in a chicken entrée? Explain your reasoning.
  1. When asked to find a “typical” amount of cholesterol in a burger, Meliva, Kyle, and Yu responded with different answers. (Refer to page 33 for their answers)

a. If Meliva, Kyle, and Yu continued their same line of thinking, what would each say about the amount of cholesterol in a “typical” chicken entrée?

Meliva:

Kyle:

Yu:

b. Did any one of the three give a better answer than the other two? Why or why not?

c. Whose answer could help you determine if most brands of burgers have 85 mg of cholesterol or more? Explain your reasoning.

d. Why is Kyle’s answer greater than Meliva’s?

3. The histogram on the top of page 35 shows the ages of the actresses whose performances won in the Best Leading Role category at the annual Academy Awards (Oscars). Estimate the mean age of the winners.

4. The histogram on the middle of page 35 shows a set of 40 values.

a. How many 5s are there in this set of values?

b. What is the mode of this set of values?

c. Find the median of this set of values. Locate the median on the horizontal axis of the histogram.

d. Find the area of the bars to the left of the median.

e. Find the area of the bars to the right of the median.

f. What do you conclude about the location of the median on a histogram?

g. Estimate the mean of the distribution by estimating the balance point of the histogram.

h. Find the mean using your calculator or computer. How close was your estimate in Part g?

5. Once data has been entered into your calculator or computer, you can calculate measures of center quickly.

a. Use your calculator or computer to find the mean number of milligrams of cholesterol in the chicken items. Mark the mean on the steam-and-leaf plot you prepared in Activity one.

b. Use your calculator or computer to find the median number of milligrams of cholesterol. Mark the median on the plot.

c. With a partner, explore other ways of calculating the median number of milligrams of cholesterol on your calculator or computer using sorted ideas.

d. Most technological tools have no operation for calculating the mode of a distribution. Explain how sorting data would make the process determining a mode easier.

e. Using data lists on your calculator or computer, find the minimum and the maximum amounts of cholesterol in the chicken items.

6. Find the mean and median of the following set of values.

1, 2, 3, 4, 5, 6, 70

Mean: ______Median: ______

a. Change the outlier 70 to 7. Then find the mean and median of the new set of values. Which changed more, the mean or the median?

Mean: ______Median: ______

b. Is the mean or the median more resistant to outliers? Explain your reasoning.

c. Is the mode resistant to outliers? Why or why not?

7. Describe a situation where it would be better if the teacher uses the median test score when computing your grade. Describe a situation where the mean is better.

8. Refer back to page 22 for the data and complete the following.

a. Find the mean and median of each distribution. Divide up the work within your group. Using different colored pencils or pens, locate and label the mean and median on the horizontal axis of each histogram.

Mean / Median
Total Calories
Fat (grams)
Cholesterol (mg)

b. Locate the mean and median on the histograms below:




c. Class Discussion (Think about the relationship between the mean and the median for distributions that are normal, skewed left and skewed right.)


Checkpoint

  1. Compare a stem-and-leaf plot to a histogram. How are they alike and how are they different?
  1. How does a back-to-back stem-and-leaf plot help you compare two distributions?
  1. Describe three methods of estimating a “typical” value for a distribution.

Course 1 Unit 1 Lesson 2 Investigation 3Page 1 of 6