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Lesson 8 Contents Objective #1: Use the Mean, Median, and Mode as measures of central tendency Example 1Find the Mean, Median, and Mode Example 2Use a Line Plot Example 3Find Extreme Values that Affect the Mean Objective #2: Analyze data using mean, median, and mode Example 4Use, Mean, Median, and Mode to Analyze Data Example 5Work Backward

Lesson 8 Contents Practice and Apply Objective #1: Use the Mean, Median, and Mode as measures of central tendency odd even (Alt. 11, 15) Objective #2: Analyze data using mean, median, and Mode 17 Maintaining Your Skills 23-31

Example 8-1a Movies The revenue of the 10 highest grossing movies as of June 2000 are given in the table. Find the mean, median, and mode of the revenues. Answer: The mean revenue is $379.8 million. Top 10 Movie Revenues (millions of $) Objective #1: Use the Mean, Median, and Mode

Example 8-1a To find the median, order the numbers from least to greatest. Answer: The median revenue is $343.5 million. 290, 306, 309, 313, 330, 357, 400, 431, 461, 601 Answer: There is no mode because each number in the set occurs once. There is an even number of items. Find the mean of the two middle numbers. Objective #1: Use the Mean, Median, and Mode

Example 8-2a Olympics The line plot below shows the number of gold medals earned by each country that participated in the 1998 Winter Olympic games in Nagano, Japan. Find the mean, median, and mode for the gold medals won. Answer: The mean is Objective #1: Use the Mean, Median, and Mode

Example 8-2a There are 24 numbers. The median number is the average of the 12 th and 13 th numbers. Answer: The median is 2. The number 0 occurs most frequently in the set of data. Answer: The mode is 0. Objective #1: Use the Mean, Median, and Mode

Example 8-3a Quiz scores The quiz scores for a math class are 8, 7, 6, 10, 8, 8, 9, 8, 7, 9, 8, 0, and 10. Identify an extreme value and describe how it affects the mean. The data value 0 appears to be an extreme value. Calculate the mean with and without the extreme value to find how it affects the mean. mean with extreme valuemean without extreme value Answer: The extreme value 0 decreases the mean by 8.2 – 7.5 or about 0.7. Objective #1: Use the Mean, Median, and Mode

Example 8-1b Objective #1: Use the Mean, Median, and Mode

Example 8-1b Test Scores The test scores for a class of nine students are 85, 93, 78, 99, 62, 83, 90, 75, 85. Find the mean, median, and mode of the test scores. Answer: mean, 83.3 ; median, 85 ; mode, 85 Objective #1: Use the Mean, Median, and Mode

Example 8-2b Families A survey of school-age children shows the family sizes displayed in the line plot below. Find the mean, median, and mode. Answer: mean, 4.3 ; median, 5 ; mode, 5 Objective #1: Use the Mean, Median, and Mode

Example 8-3b Birth Weight The birth weights of ten newborn babies are given in pounds: 7.3, 8.4, 9.1, 7.9, 8.8, 6.5, 7.9, 4.1, 8.0, 7.5. Identify an extreme value and describe how it affects the mean. Answer: 4.1 ; it decreases the mean by about 0.4. Objective #1: Use the Mean, Median, and Mode

Bob’s Books The Reading Place Example 8-4a The table shows the monthly salaries of the employees at two bookstores. Find the mean, median, and mode for each set of data. Based on the averages, which bookstore pays its employees better? mean: Bob’s Books median: 1290, 1400, 1400, 1600, 3650 median mode: $1400 Objective #2: Analyze data

Bob’s Books The Reading Place Example 8-4a mean: The Reading Place mode: none median: 1400, 1450, 1550, 1600, 2000 median Answer: The $3650 salary at Bob’s Books is an extreme value that increases the mean salary. The employees at The Reading Place are generally better paid as shown by the median. Objective #2: Analyze data

Example 8-5a Grid–In Test Item Jenny’s bowling average is 146. Today she bowled 138, 140, and 145. What does she need to score on her fourth game to maintain her average? Read the Test Item Find the sum of the first three games. Then write an equation to find the score needed on the fourth game. Objective #2: Analyze data

Example 8-5a Solve the Test Item Step 1Find the sum of the first three games x. mean of the first three scores Multiply each side by 3. Simplify. sum of first three scores Objective #2: Analyze data

Example 8-5a Step 2 Find the fourth score, x. mean Write an equation. Multiply each side by 4 and simplify. Subtract 423 from each side and simplify. Substitution. Objective #2: Analyze data

Example 8-5a Answer: Jenny needs to score at least 161 to maintain her average of 146. Objective #2: Analyze data

Example 8-4b Objective #2: Analyze data

MenWomen Example 8-4b The number of hours spent exercising each week by men and women are given in the table. Find the mean, median, and mode for each set of data. Based on the averages, which gender exercises more? Answer: Men: mean, 5.7 ; median, 4.5 ; mode, none Women: mean, 3.7 ; median, 3 ; mode, 1 Men seem to exercise more. Objective #2: Analyze data

Example 8-5b Emily scored 73, 82, and 85 on her first three math tests. What score does Emily need on the fourth test to give her an average of 82 for the four tests? Answer: 88 Objective #2: Analyze data

End of Lesson 8