Name______
A Healthy Breakfast
Which breakfast cereals are the most healthy? List three cereals that you think are very healthy.
______
Is there any marketing strategy used in the placement of cereals on grocery store shelves?
Are cereals that are high in sugar also high in fat?
Do hot cereals have more fiber than cold cereals?
In this activity we will try to find answers to these questions and others using a data file that contains nutritional information and grocery shelf location for 77 breakfast cereals.
The data includes: Manufacturers Key:
cereal name A = American Home Food Products
cereal manufacturer G = General Mills
type (hot or cold) K = Kelloggs
number of calories per serving N = Nabisco
grams of protein P = Post
grams of fat Q = Quaker Oats
milligrams of sodium R = Ralston Purina
grams of fiber
grams of carbohydrates
grams of sugars
milligrams of potassium
typical percentage of the FDA's RDA of vitamins
the weight of one serving
the number of cups in one serving
shelf location (1,2 or 3 for bottom, middle or top).
A “rating” calculated by Consumer Report
Lab
1. Getting Started
Open Fathom and drag a new collection box on to the workspace. Go to Internet Explorer and enter:
http://lib.stat.cmu.edu/DASL/Datafiles/Cereals.html
You should see the page with the Datafile Name: Cereals. Reduce the size of the Internet Explorer window. Highlight the web address and then click and drag this address into the new collection box on your Fathom workspace. Drag a new case table on to the workspace. This case table should now have all the data for the 77 breakfast cereals.
2. Dot Plots
Drag a new graph on to the workspace. Drag the column heading for Salt and drop it on the horizontal axis. Create 5 more graphs with sugar, fiber, fat, calories, and rating on the horizontal axis. Arrange the graphs so that you can see all 6 at once.
Questions/Discussion:
Ø 1. On the salt graph, double click on the point for the cereal with the highest salt content. The Inspect Cereals Box comes up. What is the name of the cereal with the highest salt content? Close the Inspector Box.
Ø 2. What is the cereal with the highest fiber content?
Ø 3. Notice that when you click on the point for the cereal with the highest fiber content, a point corresponding to that Cereal turns red on each of the other. How does the cereal with the highest fiber compare to other cereals for sugar, fat, calories, sodium and rating?
Ø 4. On the fiber graph, click and drag a rectangle to capture the three right most points. Do the conclusions you made in 3 above apply for all three of these cereals? Explain.
3. Scatterplots
Make a scatterplot with fiber on the x-axis and rating on the y-axis. Make three more graphs with rating on the y-axis, but using sugar, fat and sodium on the x-axis.
Question/Discussion:
Ø 5. Do you see a relationship between ratings and each of the categories: sugar, sodium, fiber and fat? Describe the relationship. Copy each of these graphs into your Word document.
4. Box Plots and Summary Tables
Drag a new graph on to the workspace. While holding down the shift key, click and drag the Shelf column heading to the y-axis. Holding down the shift key converts the numerical data in this column to categorical data. Drag the Sugar column heading to the x-axis. (Do not hold down the shift key.) Change the graph from a dot plot to a box plot.
Next, drag a new Summary Table down on to the workspace. Holding the shift key, click and drag the Shelf column heading to the right arrow. Click and drag the Sugar column heading to the down arrow.
Questions/Discussion
Ø 6. Which shelf has cereals with the highest sugar content? What is the mean and median sugar content for this shelf? Why do you think this shelf has the cereals with the highest sugar content?
Ø 7. Which shelf has the highest variability in sugar content? What is the range and iqr for this shelf?
Ø 8. Which shelf has the most symmetric distribution for sugar content of cereals?
Copy the box plots and summary table to your Word document.
5. Outliers
Drag a new graph on to the workspace. Drag and drop the sugar column heading on to the x-axis. Change the graph to a histogram. Click the right mouse button and select Plot Value from the menu. Type mean ( ) and click OK. A line should appear on the graph where the mean is and the value of the mean appears in the lower left hand corner below the graph. Repeat this process again, but this time type median ( ).
Question/Discusion
Ø 9. What is the mean and median sugar content for all cereals? How do the mean and median compare to each other.
Now got to Cereal Case table and scroll down below the 77th entry. On the 78th line lets enter a new cereal called Sweeties. Type Sweeties and then Tab over to the sugar column and enter a 50. Sweeties have a very high sugar content compared to the other cereals.
Ø 10. Look back at the graph for sugar. What has happened to the mean? What has happened to the median? Which is effected more by an outlier: the median or the mean?
Lets remove Sweeties before we continue. On the case table, point at the entry number 78 in front of the Sweeties. Right click and select Cut Case. The Sweeties case should now be gone.
Final Questions/Discussion
For each of the questions below, support your answer with both graphs and statistics (mean, median, range, etc.)
Ø 11. Are the three cereals that you listed at the start of this activity amongst the healthiest cereals?
Ø 12. Do hot cereals have more fiber than cold cereals?
Ø 13. Your family doctor recommends that your father go on a low salt diet. Which cereal manufacturers produce cereals that are low in sodium?
Ø 14. Are cereals that are high in sugar also high in fat?
Ø 15. Create a histogram for the cereal ratings. Describe this distribution in terms of shape, center and spread.
Ø 16. Is there any particular cereal manufacturer who produces cereals that are rated higher on average than those cereals produced by the other manufacturers?