CC Course 1 Homelogout

CC Course 1 Home Logout  Introduction  Chapter 1  Chapter 2  Chapter 3  Chapter 4  Chapter 5  Chapter 6  Chapter 7  Chapter 8 o 8 Opening o 8.1.1 o 8.1.2 o 8.1.3 o 8.1.4 o 8.1.5 o 8.2.1 o 8.3.1 o 8.3.2 o 8.3.3 o 8 Closure  Chapter 9  Reference  Teacher  Lesson (ENG)  Lección (ESP)  Answers  Teacher Notes  My Notes  Sharing [Hide Toolbars] 

 To continue your investigation of how to describe and represent data, today you will analyze the shape and spread of the data. As you work with your team, ask yourself these questions.  How can I compare data?  What measures can help me compare data?  Is there a better way to describe or represent the data?  8-30. Mrs. Ross is the school basketball coach. She wants to compare the scoring results for her team from two different games. The number of points scored by each player in each of the games are shown below.  Game 1: 12, 10, 10, 8, 11, 4, 10, 14, 12, 9 Game 2: 7, 14, 11, 12, 8, 13, 9, 14, 4, 8 1. How many total players are on the team? 2. What is the mean number of points per player for each game? 3. What is the median number of points per player for each game? 4. What is the range of points for each game? 5. With your team, discuss and find another method for comparing the data. 6. Do you think the scoring in two games is equivalent?  8-31. Using the data from problem 8-30, create histograms for both Game 1 and Game 2. Make intervals of 2 points. How are the games different?  8-32. HOW CAN I MEASURE SPREAD?  One way to measure the spread of data (how much variability there is in the data) is to calculate the range. However, part (d) of problem 830 shows that this measure may not provide a true sense of the spread.  A better way to measure the spread of the data is to calculate the mean absolute deviation. Read the Math Notes box in this lesson for an explanation of mean absolute deviation. Then follow the steps below to compute the mean absolute deviation for the basketball games. 1. Data value Difference Absolute from mean value 12 2 2

9 −1 1 sum: 2. Copy the table at right. Then use it to calculate the mean absolute deviation for Game 1 of problem 8-30 by following the steps below. Two of the rows are completed for you. 2.1. List the data values in the first column. 2.2. In the second column, list the differences when the mean is subtracted from each value. 2.3. List the absolute value of the differences in the third column. 2.4. Calculate the sum of the third column (the absolute values). 2.5. Divide the sum by the number of data values in the set to find the mean absolute deviation. 3. Repeat the process from part (a) to calculate the mean absolute deviation of the data from Game 2 in problem 8-30. 4. Does this method of showing the average (mean) distance from the mean help to distinquish between the two games? How?  8-33. Did you notice how absolute value was used to calculate the mean deviation in the previous problem? What would happen if you did not use absolute value? Use your data to demonstrate what would happen if absolute value was not used.  8-34. Why is it appropriate to use a mean instead of a median to analyze each of the basketball games from problem 8-30?  8-35. HOW CAN I DESCRIBE THE SHAPE?  Statisticians use the words below to describe the shape of data distribution. Use your vocabulary skills, and the glossary if you need it, to match the terms with the histograms that follow. Note that each histogram is described using two terms.  DOUBLE-PEAKED SINGLE-PEAKED SKEWED SYMMETRIC UNIFORM 1.  8-36. Look at the histograms you created in problem 8-31. Which words from problem 835 can you use to describe them?  Score Frequency 1 1 2 5 3 12 4 15 5 11 6 4 7 2  8-37. The set of data at right is organized in a frequency table. 1. If you were to create a dot plot of this data, how would you describe the shape using the words listed in problem 8-35? 2. How many total scores are there? 3. Using the table, calculate the sum of all of the scores. 4. Is it appropriate to calculate the mean? Why or why not? If so, what is the mean?

5. Calculate the mean absolute deviation using the method from problem 831. 6. Additional Challenge: Is there a different way to set up the table so that you do not have to list all of the data points individually?  8-38. LEARNING LOG  Write a Learning Log entry that describes mean absolute deviation in your own words. Under what circumstances is it appropriate to calculate a mean absolute deviation? Title this entry “Mean Absolute Deviation” and include today’s date. 

Mean Absolute Deviation  One method for measuring the spread (variability) in a set of data is to calculate the average distance each data point is from the mean. This distance is called the mean absolute deviation. Since the calculation is based on the mean, it is best to use this measure of spread when the distribution is symmetric.  For example, the points shown below left are not spread very far from the mean. There is not a lot of variability. The points have a small average distance from the mean, and therefore a small mean absolute deviation.

  The points above right are spread far from the mean. There is more variability. They have a large average distance from the mean, and therefore a large mean absolute deviation.

 8-39. Assume that the histograms below represent the amount of time it took two different groups of 100 people to run a 5K race. Assume that the mean of each histogram is the same. Which group has a greater mean absolute deviation? Why? Homework Help ✎   8-40. Describe the shape of the distributions in problem 8-39 above using the vocabulary list in problem 8-35. Homework Help ✎

 8-41. Kayla had a 14-foot rope that she cut into three pieces. Now two of the pieces are the same length, and the third piece is 2 feet long. Homework Help ✎ 1. Copy Kayla’s diagram below onto your paper and write an equation that represents the situation. Be sure to remember to define your variable. 2. Solve your equation and find the length of each of the two equal pieces.

 8-42. Complete a portions web for each of the following fractions. Homework Help ✎

 8-43. Solve and graph the following inequalities: Homework Help ✎ 1. x − 9 < 17 2. x + 12 ≤ 6 3. 10 ≥ 4 + x [Hide Toolbars]

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