Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Session 3, Part D:
Ordering Hats

In This Part: Understanding the Question | Data Analysis Using a Stem and Leaf Plot
Using a Histogram to Analyze the Hat-Size Data | Summary

The stem and leaf plot for this data set looks like this:

Problem D7

Use the stem and leaf plot to determine the following:

 a. The grouped frequency and relative frequency tables for the head-circumference data b. The frequency histogram for the head-circumference data

 Problem D8 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?

 Problem D9 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?"

 Problem D10 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?

Problem D11

Based on these data, plan an order for 1,000 Standard Fit hats.

Standard Size

Fits Circ. (mm)

Number To Order

 S1 520 to < 530 S2 530 to < 540 S3 540 to < 550 S4 550 to < 560 S5 560 to < 570 S6 570 to < 580 S7 580 to < 590 S8 590 to < 600 S9 600 to < 610 S10 610 to < 620

Size

Number To Order

 S1 18 S2 36 S3 55 S4 200 S5 218 S6 109 S7 109 S8 73 S9 145 S10 36

 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 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.

Problem D12

Using frequency computations, the total number of hats might not be exactly 1,000.

 a. Why did this happen? b. To complete the order of 1,000, for which size would you order one more?

 Problem D13 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 It may help to recall that this is a unisex "Standard Fit" hat size.

 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.

Problem D14

Use these same data to plan an order for two more hat styles:

 a. Loose Fit: Five hat sizes; hat sizes are separated by 20 mm. b. Exclusive Fit: 20 hat sizes; hat sizes are separated by five mm.

 Session 3: Index | Notes | Solutions | Video