# Problem of the Month Pick a Pocket

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2 situation. In the final levels of the POM, students examine data in situations that require statistical tools other than measures of center. In the context of these situations, students focus on measures of dispersion and the distribution of data.

3 Level A: Examine the number of pockets each student in your class is wearing. Count the number of pockets worn by each student. Make a table of the number of pockets worn by each student. Draw a graph using the data from the table. What is the largest amount of pockets worn by a student? What is the smallest number of pockets anyone wore? What is the total number of pockets worn by all the students? Tomorrow, if we surveyed the class would we have the same number of pockets? Explain. Problem of the Month Page 1 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported License (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_us).

5 Level C: In Dia s class they made a line plot of the different number of pockets worn by the students. X X X X X X X X X X X X X X X X X X X X Each student wrote what they thought was the typical number of pockets for a student in their class. Explain why you think each statement does or does not make sense mathematically. Raul: I think 3.7 is typical because I found the average by adding the numbers that have X s on them like = 26 and 26 divided by the 7 numbers = 3.7 Joanne: I found the median but first I ignored each zero, since they don t have pockets. Therefore, there are 17 other X s and the ninth one would be in the middle. I started counting X s from the right side moving left and I landed on the X over the number 4. So, I think 4 pockets are typical for our class. Austin: I think 8 pockets are way out of the normal range, so I am going to ignore it. Therefore, the numbers of pockets go from 0 to 6 and (0 + 6)/2 = 3. Therefore, 3 is my choice for most typical, because it is in the middle. Ming: I calculated the following way to find an answer. 3 x x x x x x x 8 = / 20 = 3.1 I think 3 is typical. Problem of the Month Page 3 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported License (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_us).

6 Level D: You just got a new video game called Drop in the Pocket. It simulates a new type of game of pool. There is one pocket (hole) in the middle of the table. You hit a ball from a starting point trying to sink it in the pocket. If you miss it, the game tells you how many millimeters you are from the pocket. You and your two friends each try playing by taking turns for five rounds. None of you actually makes it in the pocket. At the end of the round the game shows the results. Round Player A Player B Player C Use mathematics to determine who was the best player over the five rounds. Explain a method or system that might be used to judge a winner or keep score of the game. Problem of the Month Page 4 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported License (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_us).

7 Level E: You are a manager for a clothing manufacturer. You work in the department that makes denim pants. You have workers who sew pockets onto the pants. You want to give one of them the Employee of the Month award. So for twelve days you track the number of pants they sew each day. Below are the numbers of completed pants by the two most productive employees for each of the 12 days. Use mathematics to determine which of the two employees should get the award. Remember you might have to explain to the other employee why he didn t get chosen, so you must use a mathematical measure to be most objective. Day Employee Ariana Employee Brian Problem of the Month Page 5 This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 Unported License (http://creativecommons.org/licenses/by-nc-nd/3.0/deed.en_us).

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