1 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?

2 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 a)How many total players are on the team? b)What is the mean number of points per player for each game? c)What is the median number of points per player for each game? d)What is the range of points for each game? e)With your team, discuss and find another method for comparing the data. f)Do you think the scoring in two games is equivalent? 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?

3 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 8 ‑ 30 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. Copy the table from page 390. 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. a)List the data values in the first column. b)In the second column, list the differences when the mean is subtracted from each value. c)List the absolute value of the differences in the third column. d)Calculate the sum of the third column (the absolute values). e)Divide the sum by the number of data values in the set to find the mean absolute deviation. Repeat the process from part (a) to calculate the mean absolute deviation of the data from Game 2 in problem Does this method of showing the average (mean) distance from the mean help to distinguish between the two games? How?

4 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. 34. Why is it appropriate to use a mean instead of a median to analyze each of the basketball games from problem #30? 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

5 Score Frequency Look at the histograms you created in problem Which words from problem 8 ‑ 35 can you use to describe them? 37. The set of data at right is organized in a frequency table. a)If you were to create a dot plot of this data, how would you describe the shape using the words listed in problem #35? b)How many total scores are there? c)Using the table, calculate the sum of all of the scores. d)Is it appropriate to calculate the mean? Why or why not? If so, what is the mean? e)Calculate the mean absolute deviation using the method from problem 8 ‑ 31

6 38. LEARNING LOG Write a Learning Log entry that describes in your own words… a) mean b)absolute deviation. c)Under what circumstances is it appropriate to calculate a mean absolute deviation? Title this entry “Mean Absolute Deviation” and include today’s date.

7 Tonight’s homework is… Review & Preview, problems #39-43 Show all work and justify your answers for full credit.