Use the stem and leaf plot to determine the following:
The grouped frequency and relative frequency tables for the head-circumference data
The frequency histogram for the head-circumference data
What information in the data is "lost" when the distribution is represented by a grouped frequency table and histogram instead of a stem and leaf plot?
What can you say about the way head sizes are distributed? Based on the grouped relative frequency table and the histogram, give two descriptive statements to answer the question "How large are people's heads?"
Based on the grouped frequency table and the histogram, do some head sizes appear to be more common than others? Which head sizes are most common? Least common?
Based on these data, plan an order for 1,000 Standard Fit hats.
You will need to convert the relative frequencies into quantities of hats, adding up to 1,000. If you listed the frequencies as percentages, your data are already represented as portions of 100. Think about how you might convert your data so that they represent portions of 1,000. Close Tip
Using frequency computations, the total number of hats might not be exactly 1,000.
Why did this happen?
To complete the order of 1,000, for which size would you order one more?
Do you see anything unusual in the variation illustrated in the stem and leaf plot and the relative frequency histogram? Can you think of a reason for this unusual pattern?
It may help to recall that this is a unisex "Standard Fit" hat size. Close Tip
Video Segment In this video segment, participants use a stem and leaf plot to analyze head-circumference data collected by the class. Based on what they see, they revise their initial expectations for the distribution of hat sizes. Watch this segment after completing Problem D13.
Note: The data set used by the onscreen participants is different from the one provided above.
What might one expect the middle values to be like? What accounts for the unexpected results?
If you're using a VCR, you can find this segment on the session video approximately 13 minutes and 31 seconds after the Annenberg Media logo.