3. Advise Josh Which Club to Use. Explain Your Thinking

Lesson 8.1.2

HW: 8-23 through 8-28

Learning Target: Scholars will compare two populations based on making inferences from samples. Scholars will quantify the difference between the medians as a multiple of the IQR.

In Lesson 8.1.1, you compared the results of two different methods of measuring to answer the question, “Which measuring tool is more precise?” Today you will continue to develop your methods for comparing two distributions of data.

8-19. Josh is just starting a round of golf. This first hole is 130 yards long. He needs to decide which club to use for his first shot. He has kept careful records about how close his first shots came to the hole, all from this same distance. His records include data from his use of two different golf clubs, a wedge and an 8-iron, over the past year. Wedge, distance to hole (yards): 0 3 1 2 7 2 15 25 5 22 8-iron, distance to hole (yards): 19 12 12 8 3 11 5 7 10 13 8 10 11 20 1. Create a histogram and box plot for each of the clubs. Place the box plot above the histogram on the same number line for each club to make a combination plot. Use a bin width of 5 yards. 2. To find the “typical” distance that Josh hits the ball from the hole with a wedge, is the mean or the median a better choice? Find the typical distance Josh hits the ball from the hole with a wedge and compare it to the typical distance he hits the ball with an 8-iron. 3. Advise Josh which club to use. Explain your thinking.

8-20. It is just as important to consider the spread of the data as it is to consider the center when comparing data sets. 4. Calculate the Interquartile Range (IQR) for each golf club in the previous problem. With which club is Josh more consistent? 5. If Josh decided to use the 8-iron, he could "typically" expect to hit the ball so that it lands between 8 and 12 yards from the hole. This is indicated by the box on the box plot display and corresponds with the IQR. If Josh decided to use the wedge, what is a “typical” interval of distances from the hole he could expect the ball to land? 6. Compare the typical interval of distances for the 8-iron with the interval you found for the wedge. Do you wish to modify your advice to Josh? Explain. 8-21. Mr. Webb has only one more starting position available on his basketball team, but two students have tried out for it. He wants to choose the student who is likely to score the most points. The two students from whom he can choose are described below. 7. In her most recent games, Jana scored: 7 46 9 6 11 7 9 11 19 7 9 11 9 55 11 7 points, while Alejandra scored 13 15 9 18 13 17 17 15 points. Which girl has the higher average (mean) number of points? 8. Which student do you think Mr. Webb should select and why? Use parallel box plots (two box plots on the same number line) to support your explanation. 9. Why was the mean not a good measure of the girl’s typical performance? 10. Calculate the IQR to measure the variability of each girl’s performance. 11. Who had the higher median and by how many points? How large is the difference between the medians measured by how many IQRs would fit into it?

8-22. Gregory and his sister shared a computer at home. In order to be fair, they kept track of how much time they spent socializing with friends each day for the last two weeks. Their usage in minutes follows: 1. Gregory: 49 48 51 52 68 40 73 68 61 60 69 55 51 59 2. His sister: 49 45 37 63 56 57 62 50 42 48 55 64 40 42 Make a parallel box plot to compare their usage. Is their median usage notably different from each other? If the usage is notably different, how much more did one of them use the computer than the other, measured in number of IQRs?

8-23. The two histograms below show how precisely Lue threw 50 darts with his right hand and then 50 with his left hand. Study the two histograms. 1. Estimate what the box plots would look like and make a parallel box plot. 2. Compare the center, shape, spread, and outliers between Lue’s left hand and right hand. 3. Is Lue more precise throwing with his right hand or with his left hand? 4. Use the box plot to estimate how many IQRs above the median Lue’s better hand is. Explain your thinking.

8-24. Find the missing lengths or values on the diagram below. Assume that the line is evenly divided.

8-25. Joaquin has agreed to lend his younger brother $45 so that he can buy a new tank for his pet lizard. Joaquin is charging his brother 2% simple interest per month. If his brother pays him back in 6 months, how much will Joaquin get back? 8-26. Michaela holds her state high school record for the 500-meter freestyle swimming event. She can swim the event in 4 minutes and 50 seconds. At this same rate, how far will she swim in 10 minutes?

8-27. Mrs. Chen has two brothers. Mark is 7 years older than Mrs. Chen and Eric is 11 years younger than Mrs. Chen. The sum of all three of their ages is 149. Use the 5-D Process to determine the age of Mrs. Chen. 8-28. For each equation below, solve for x. Show the process you use to check your answer.

5. 6. 5x = 2x + 12 7. x − 14.6 = 8.02

Lesson 8.1.2  8-19. See below: 1. See plots below. 2. Median since the distribution is not symmetrical. Wedge median is 4 yards, and 8-iron median is 10.5 yards; on average he is 6.5 yards closer with the wedge. 3. Possible answer: Josh should use the wedge. The median is much closer to the hole; some students may be thinking about the consistency also, which is an excellent preview to the next problem.  8-20. See below: 1. Wedge IQR is 13, and 8iron IQR is 4. Josh is much more consistent with the 8- iron. 2. Between the first and third quartile, between 2 yards and 15 yards from the hole. 3. The typical interval of distances for the 8-iron is in the middle of the wedge interval. So the 8-iron is not so clearly different from the wedge. If there is a hazard very close to the hole, Josh may prefer the consistency of the 8iron.  8-21. See below: 1. They are both the same, 14.625 points. 2. Alejandra typically scores more points; the top 75% of Alejandra’s scores are all higher than the bottom 75% of Jana’s scores; see parallel box plot below.

3. Jana’s scores are not symmetrical. 4. 4 for each girl. 5. Alejandra’s median, 15, was 6 points higher than Jana’s, 9. Alejandra outperformed Jana by 1.5 IQRs.  8-22. See box plot below. Gregory’s median usage (57, IQR = 17) is about one half IQR longer than his sister’s (49.5, IQR = 15).  8-23. See below: 1. See solution plot below.

2. With his left hand, Lue’s median shot is 5 or 6 inches closer to the bull’s eye; with his right hand, the distribution of Lue’s shots is symmetric and single peaked; with his left hand, the distribution is skewed with a peak at the bull’s-eye; Lue has more tosses closer to the bull’s-eye with his left hand; IQR for left hand is about 4.5; neither hand threw any outliers, but students may feel that 14 is an outlier for the left hand. 3. Lue throws more consistently with his left hand because the IQR is smaller on the box plots. 4. About one IQR.  8-24. a = 0.3, b = 0.4, c = 40%, d = 15%  8-25. $50.40  8-26. She will swim 1034.48 meters.  8-27. Mrs. Chen is 51 years old.  8-28. See below:

1. x = 3 2. x = 4 3. x = 22.62