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Data Session 3 Solutions
 
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A B C D 
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Solutions for Session 3, Part D

See solutions for Problems: D1 | D2 | D3 | D4 | D5 | D6| D7| D8| D9
D10| D11| D12| D13| D14


Problem D1

Answers will vary. One possible answer is that fewer people will have especially large or especially small head sizes, just as there are fewer people who are especially tall or short. This might suggest that the fifth and sixth (i.e., the middle) sizes would be the most common.

<< back to Problem D1


 

Problem D2

Measure your head and find out!

<< back to Problem D2


 

Problem D3

Here is the completed stem and leaf plot:

completed stem and leaf

<< back to Problem D3


 

Problem D4

 

All heads are between 520 and 615 mm.

 

There is a range of 95 mm, which indicates a lot of variation in head circumferences.

 

Thirty-five of the 55 head circumferences (63.6%) are between 550 and 587 mm, a range of 37 mm.

 

Twenty-three of the 55 head circumferences (41.8%) are between 550 and 569 mm, a range of only 19 mm.

<< back to Problem D4


 

Problem D5

Head sizes between 550 and 569 mm are the most common. Head sizes below 540 mm and above 610 mm are the least common.

<< back to Problem D5


 

Problem D6

You would quickly sell out of the more common sizes and have many of the least common sizes still on hand.

<< back to Problem D6


 

Problem D7

Head Circ. (mm)

Frequency

Relative Frequency (%)

520 to < 530

1

1.8

530 to < 540

2

3.6

540 to < 550

3

5.5

550 to < 560

11

20.0

560 to < 570

12

21.8

570 to < 580

6

10.9

580 to < 590

6

10.9

590 to < 600

4

7.3

600 to < 610

8

14.5

610 to < 620

2

3.6

Note that the relative frequencies add up to 99.9%, due to rounding.

historgram

<< back to Problem D7


 

Problem D8

You no longer have the actual data values, only the number of values within intervals of 10 millimeters.

<< back to Problem D8


 

Problem D9

Answers will vary, but here are some observations:

 

All heads are between 520 and 620 mm.

 

There is a range of 100 mm, which indicates a lot of variation in head circumferences.

 

Thirty-five of the 55 head circumferences (63.6%) are between 550 and 590 mm, a range of 40 mm.

 

Twenty-three of the 55 head circumferences (41.8%) are between 550 and 570 mm, a range of only 20 mm.

<< back to Problem D9


 

Problem D10

Head sizes between 550 and 570 mm are the most common. Head sizes below 540 mm and above 610 mm are the least common.

<< back to Problem D10


 

Problem D11

Perform this by expressing the relative frequency as a decimal, then multiplying this decimal by 1,000. (If you wanted to work with the percentage value without converting it to a decimal, you need to remember that percentages are per 100, so you would need to multiply the percentage value by 10 to find the number per 1,000.)

Size

Number To Order

S1

18

S2

36

S3

55

S4

200

S5

218

S6

109

S7

109

S8

73

S9

145

S10

36

<< back to Problem D11


 

Problem D12

a. 

You should have found a total of only 999 hats, due to the rounding in the relative frequencies from Problem D7.

b. 

Answers will vary. One possible answer is to use S4 or S5, since they are the most common sizes. Another is to use either S3 or S9, since the numbers of hats in these sizes when written as decimals are closest to being rounded up (S9, for example, would be 145.4545... hats).

<< back to Problem D12


 

Problem D13

Yes. There are two distinct peaks in the histogram, which may be due to the fact that male and female head sizes are mixed together in this data set. This raises several questions: Do men and women have similar-sized heads? If not, do men tend to have larger heads than women, or do women tend to have larger heads than men?

<< back to Problem D13


 

Problem D14

To calculate these answers, you will first need to set the hat sizes, then use the data values to determine the relative frequency of the hat sizes you selected, then multiply these frequencies expressed as decimals by 1,000 to determine how many of each you will order. Answers will vary, due to the flexibility in selecting the intervals for the hat sizes.

<< back to Problem D14

 

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