1. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 1 Chapter 7 Data, Graphs, and Statistics

2. CHAPTER Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 2 7 Data, Graphs, and Statistics 7.1Averages, Medians, and Modes 7.2Interpreting Data from Tables and Graphs 7.3Interpreting and Drawing Bar Graphs and Line Graphs 7.4Interpreting and Drawing Circle Graphs

3. OBJECTIVES Copyright © 2015, 2011, and 2008 Pearson Education, Inc. 3 7.1 Averages, Medians, and Modes aFind the average of a set of numbers and solve applied problems involving averages. bFind the median of a set of numbers and solve applied problems involving medians. cFind the mode of a set of numbers and solve applied problems involving modes.

4. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 4 A statistic is a number describing a set of data. The most common kind of center point is the arithmetic mean, or simply the mean. This center point is often referred to as the average.

5. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 5 Average To find the average of a set of numbers, add the numbers and then divide by the number of items of data.

6. 6 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Roberto bowled a 175, 210 and 162. Find his bowling average. Solution To find the mean we add the scores together and then divide by the number of scores, 3: Roberto’s bowling average is 182.

7. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 7 In most colleges, students are assigned grade point values for grades awarded. The grade point average, is the average of the grade point values for each credit hour taken. At most colleges, grade values are assigned as follows: A: 4.0 B: 3.0 C: 2.0 D: 1.0 F: 0.0

8. 8 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Cameron earned the following grades for one semester. What was his grade point average? CourseGradeNumber of Credit Hours MathematicsA4 HistoryB4 EnglishC3 SpanishB3 BiologyC4

9. 9 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. continued Some classes carry more weight then others. His A in math could count as 4-A’s. Rather than list them all out, we will multiply and then add before dividing. Mathematics 4.0  4 = 16 History 3.0  4 = 12 English 2.0  3 = 6 Spanish 3.0  3 = 9 Biology 2.0  4 = 8 CourseGradeNumber of Credit Hours MathematicsA4 HistoryB4 EnglishC3 SpanishB3 BiologyC4 51 Multiplying grade point values by the number of credits for each course Total

10. 10 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. continued The total number of credit hours taken is: 4 + 4 + 3 + 3 + 4 = 18. We divide 51 by 18. Cameron’s grade point average was 2.833. CourseGradeNumber of Credit Hours MathematicsA4 HistoryB4 EnglishC3 SpanishB3 BiologyC4

11. 11 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example To earn an A in math, Johanna must have a mean test score of at least 90. On the first four tests, her scores were 92, 88, 95, and 81. What is the lowest score Johanna can get on the last test and still get a A? Solution We can find the total of five scores needed as follows: 90 + 90 + 90 + 90 + 90 = 450. The total of the scores on the first four tests is 92 + 88 + 95 + 81 = 357. Thus Johanna needs to get at least 450 – 356, or 94

12. 12 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. We check this as follows: continued

13. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 13 Another type of center-point statistic is the median. Medians are useful when we wish to de-emphasize unusually extreme scores. The middle number of a set of data is called the median.

14. 14 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example What is the median of this set of numbers? 89, 860, 81, 88, 116, 95, 103 Solution First we rearrange the numbers in order from smallest to largest. Then we locate the middle number. 81, 88, 89, 95, 103, 116, 860 The median is 95. Middle number

15. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 15 Median Once a set of data is listed in order, from smallest to largest, the median is the middle number if there is an odd number of values. If there is an even number of values, the median is the number that is the average of the two middle numbers.

16. 16 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example The salaries of six administrators at a large company are as follows: $72,000, $112,000, $68,000, $91,000, $71,000, $81,000. What is the median salary of the administrators? Solution Arrange the numbers in order smallest to largest. 68,000 71,000 72,000 81,000 91,000 112,000 The two middle numbers are 72,000 and 81,000.

17. 17 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. continued Median = The median salary is $76,500.

18. Copyright © 2015, 2010, and 2007 Pearson Education, Inc. 18 Mode The mode of a set of data is the number or numbers that occur most often. If each number occurs the same number of times, there is no mode.

19. 19 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the mode of these data. 23, 24, 27, 27, 18, 29 Solution The number that occurs most often is 27. A set of data has just one mean and just one median, but it can have more than one mode. It may also have no mode—when all the numbers are equally represented.

20. 20 Copyright © 2015, 2010, and 2007 Pearson Education, Inc. Example Find the mode or modes of these data: 1. 8, 12, 15, 27, 31, 42 2. 44, 55, 55, 55, 62, 65, 67, 67, 67, 72, 73, 75 Solution 1. 8, 12, 15, 27, 31, 42 There is no mode. 2. 44, 55, 55, 55, 62, 65, 67, 67, 67, 72, 73, 75 The modes are 55 and 67. 44, 55, 55, 55, 62, 65, 67, 67, 67, 72, 73, 75