1. Pre-Algebra 4-3 Measures of Central Tendency 4-3 Measures of Central Tendency Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Pre-Algebra 4-3 Measures of Central Tendency Warm Up Order the values from least to greatest. 1. 9, 4, 8, 7, 6, 8, 5, 3, 7 2. 36, 22, 35, 46, 37, 47, 30 Divide. 3. 4. 3, 4, 5, 6, 7, 7, 8, 8, 9 22, 30, 35, 36, 37, 46, 47 66 Pre-Algebra 4-3 Measures of Central Tendency 198 3 576 4 144

3. Pre-Algebra 4-3 Measures of Central Tendency Problem of the Day A mom buys a white, a green, a blue, and a yellow sweater for her 4 children. Bill and Bob refuse to wear yellow. Barb doesn’t like green, and Beth hates green and white. Mom will not put the boys in white, and Bob wont wear blue. Which sweater will each child wear? Barb:iwhite, Beth:iyellow, Bob:igreen, Bill:iblue

4. Pre-Algebra 4-3 Measures of Central Tendency Learn to find appropriate measures of central tendency.

5. Pre-Algebra 4-3 Measures of Central Tendency Vocabulary mean median mode outlier

6. Pre-Algebra 4-3 Measures of Central Tendency A measure of central tendency is an attempt to describe a data set using only one number. This number represents the “middle” of the set.

7. Pre-Algebra 4-3 Measures of Central Tendency Additional Example 1A: Finding Measures of Central Tendency Find the mean, median and the mode of the data set. A. 16, 25, 31, 14, 14, 18 mean: 16 + 25 + 31 + 14 + 14 + 18 = 118 Add the values. Divide by 6, the number of values. 118 6  19.67 median: 14 14 16 18 25 31 Order the values. 3 values 16 + 18 2 = 17 Average the two middle values. mode: The value 14 occurs two times 14

8. Pre-Algebra 4-3 Measures of Central Tendency B. 83, 45, 19, 33 mean: 83 + 45 + 19 + 33 = 180 Add the values. Divide by 4, the number of values. 180 4 = 45 median: 19 33 45 83 Order the values. 2 values 33 + 45 2 = 39 Average the two middle values. mode: No value occurs more than any other. No mode Additional Example 1B: Finding Measures of Central Tendency Find the mean, median and the mode of the data set.

9. Pre-Algebra 4-3 Measures of Central Tendency C. 21, 21, 28, 29, 30, 28, 32 mean: 21 + 21 + 28 + 29 + 30 + 28 + 32 = 189 Add the values. Divide by 7, the number of values. 189 7 = 27 median: 21 21 28 28 29 30 32 Order the values. mode: Two values occur twice. The median is 28. 21, 28 Additional Example 1C: Finding Measures of Central Tendency Find the mean, median and the mode of the data set.

10. Pre-Algebra 4-3 Measures of Central Tendency Try This: Example 1A Find the mean, median and the mode of the data set. A. 24, 31, 21, 18, 24, 22 mean: 24 + 31 + 21 + 18 + 24 + 22 = 140 Add the values. Divide by 6, the number of values. 140 6  23.33 median: 18 21 22 24 24 31 Order the values. 3 values 22 + 24 2 = 23 Average the two middle values. mode: The value 24 occurs two times. 24

11. Pre-Algebra 4-3 Measures of Central Tendency B. 81, 55, 54, 77 mean: 81 + 55 + 54 + 77 = 267 Add the values. Divide by 4, the number of values. 267 4 = 66.75 median: 54 55 77 81 Order the values. 2 values 55 + 77 2 = 66 Average the two middle values. mode: No value occurs more than any other. No mode Try This: Example 1B Find the mean, median and the mode of the data set.

12. Pre-Algebra 4-3 Measures of Central Tendency C. 45, 32, 22, 37, 45, 41, 37 mean: 45 + 32 + 22 + 37 + 45 + 41 + 37 = 259 Add the values. Divide by 7, the number of values. 259 7 = 37 median: 22 32 37 37 41 45 45 Order the values. mode: Two values occur twice. The median is 37. 37, 45 Try This: Example 1C Find the mean, median and the mode of the data set.

13. Pre-Algebra 4-3 Measures of Central Tendency An outlier is a value much greater or much less than the others in a data set.

14. Pre-Algebra 4-3 Measures of Central Tendency Additional Example 2A: Social Studies Application Use the data to find the answer. A. Find the average number of stories for the buildings that have more than 100 stories. Use the mean to answer, "What's the average?" 114 + 110 + 102 3 326 3 108.67 =

15. Pre-Algebra 4-3 Measures of Central Tendency B. Find the average number of stories for the buildings in the United States. 110 + 102 + 80 + 77 4 369 4 92.25 = Additional Example 2B: Social Studies Application Use the data to find the answer.

16. Pre-Algebra 4-3 Measures of Central Tendency C. Find the average number of stories for all of the buildings in the table. 114 + 110 + 102 + 72 + 80 + 77 6 555 6 92.5 = Additional Example 2C: Social Studies Application Use the data to find the answer.

17. Pre-Algebra 4-3 Measures of Central Tendency Try This: Example 2A Use the data to find the answer. A. Find the average number of cars crossing the borders of states beginning with the letter “A”. Use the mean to answer, "What's the average?" 119,662 + 9,904,116 2 10,023,778 2 = 5,011,889 = State Border CrossingCars crossed in 1999 Alaska119,662 Arizona9,904,116 California30,616,346 Idaho219,218 New Mexico433,416 Texas48,707,814

18. Pre-Algebra 4-3 Measures of Central Tendency B. Find the average number of cars crossing the borders of states with fewer than one million crossings. 119,662 + 219,218 + 433,416 3 772,296 3 = 257,432 = State Border CrossingCars crossed in 1999 Alaska119,662 Arizona9,904,116 California30,616,346 Idaho219,218 New Mexico433,416 Texas48,707,814 Try This: Example 2B Use the data to find the answer.

19. Pre-Algebra 4-3 Measures of Central Tendency C. Find the average number of cars crossing the borders. 119,662 + 9,904,116 + 30,616,346 + 219,218 + 433,416 + 48,707,814 6 90,000,572 6  15,000,095 = State Border CrossingCars crossed in 1999 Alaska119,662 Arizona9,904,116 California30,616,346 Idaho219,218 New Mexico433,416 Texas48,707,814 Try This: Example 2C Use the data to find the answer.

20. Pre-Algebra 4-3 Measures of Central Tendency Lesson Quiz Use the data to find each answer. 1. What is mean of Brad’s scores? 2. What is the mean of all the scores? 3. What is the mode? 4. What is the median of all the scores? 186 187 184 and 162 184.5