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Learning Math Home
Data Session 3, Part D: Counting Hats
 
Session 3 Part A Part B Part C Part D Homework
 
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Session 3 Materials:
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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:

Stem and Leaf Plot

Problem D7

Solution  

Analyze the Data:
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

Solution  

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

Solution  

Interpret Results
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

Solution  

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

Solution  

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

show answers

 

Size

Number To Order

S1

18

S2

36

S3

55

S4

200

S5

218

S6

109

S7

109

S8

73

S9

145

S10

36


hide answers


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
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

 

Problem D12

Solution  

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

Solution  

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?


Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
It may help to recall that this is a unisex "Standard Fit" hat size.   Close Tip


video thumbnail
 

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.

 

Take it Further

Problem D14

Solution

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.


 

Next > Part D (Continued): Summary

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