 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            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.   Problem D2 Measure your head and find out!   Problem D3 Here is the completed stem and leaf plot:    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.   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.   Problem D6 You would quickly sell out of the more common sizes and have many of the least common sizes still on hand.   Problem D7   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 20 560 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.    Problem D8 You no longer have the actual data values, only the number of values within intervals of 10 millimeters.   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.   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.   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    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).   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?   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.     