CHAPTER 6 Introduction to Graphing and Statistics Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 6.1Tables and Pictographs 6.2Bar Graphs and Line Graphs 6.3Ordered Pairs and Equations in Two Variables 6.4Graphing Linear Equations 6.5Means, Medians, and Modes 6.6Predictions and Probability

OBJECTIVES 6.5 Means, Medians, and Modes Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. aFind the mean of a set of numbers and solve applied problems involving means. 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. dCompare two sets of data using their means.

6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Although the word “average” is often used in everyday speech, in math we generally use the word mean instead.

6.5 Means, Medians, and Modes MEAN Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. To find the mean of a set of numbers, add the numbers and then divide the sum by the number of items of data.

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 1 Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. On a 4-day trip, a car was driven the following number of miles each day: 240, 302, 280, 320. What was the mean number of miles per day?

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 1 Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The car was driven an average of mi per day. Had the car been driven exactly mi each day, the same total distance (1142 mi) would have been traveled.

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 3Grade Point Average. Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. In most colleges, students are assigned grade point values for grades obtained. The grade point average, or GPA, is the average of the grade point values for each credit hour taken. At most colleges, grade point values are assigned as follows. A: 4.0 B: 3.0 C: 2.0 D: 1.0 F: 0.0 Meg earned the following grades for one semester. What was her grade point average?

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 3Grade Point Average. Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 3Grade Point Average. Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Because some of Meg’s courses carried more credit than others, the grades in those courses carry more weight in her GPA. To find the GPA, we first multiply the grade point value by the number of credit hours for the course.

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 3Grade Point Average. Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 6.5 Means, Medians, and Modes a Find the mean of a set of numbers and solve applied problems involving means. 3Grade Point Average. Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The total number of credit hours taken is , or 15. We divide 46 by 15 and round to the nearest tenth. Meg’s grade point average was 3.1.

6.5 Means, Medians, and Modes b Find the median of a set of numbers and solve applied problems involving medians. Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Another measure of central tendency is the median. Medians are useful when we wish to de-emphasize unusually extreme numbers. The middle number is called the median.

EXAMPLE 6.5 Means, Medians, and Modes b Find the median of a set of numbers and solve applied problems involving medians. 5 Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. What is the median of this set of numbers?

6.5 Means, Medians, and Modes MEDIAN Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Once the data in a set are 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.

EXAMPLE 6.5 Means, Medians, and Modes b Find the median of a set of numbers and solve applied problems involving medians. 6Salaries. Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. The salaries of the six employees (one of whom is the owner) of Top Notch Grill are as follows. $35,000, $29,000, $32,000, $31,000, $93,000, $30,000 What is the median salary at the restaurant?

EXAMPLE 6.5 Means, Medians, and Modes b Find the median of a set of numbers and solve applied problems involving medians. 6Salaries. Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We rearrange the numbers in order from smallest to largest. The two middle numbers are $31,000 and $32,000. Thus, the median is halfway between $31,000 and $32,000 (the average of $31,000 and $32,000):

6.5 Means, Medians, and Modes MODE Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 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.

6.5 Means, Medians, and Modes c Find the mode of a set of numbers and solve applied problems involving modes. Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. 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 numbers are equally represented. For example, the set of data 5, 7, 11, 13, 19 has no mode.

EXAMPLE 6.5 Means, Medians, and Modes c Find the mode of a set of numbers and solve applied problems involving modes. 8 Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Find the modes of these data. 33, 34, 34, 34, 35, 36, 37, 37, 37, 38, 39, 40 There are two numbers that occur most often, 34 and 37. Thus, the modes are 34 and 37.

6.5 Means, Medians, and Modes d Compare two sets of data using their means. Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Sometimes we want to know which of two groups is “better.” One way to find out is by comparing the means.

EXAMPLE 6.5 Means, Medians, and Modes d Compare two sets of data using their means. 9Growth of Wheat. Slide 22Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. A university agriculture department experiments to see which of two kinds of wheat is better. (In this situation, the shorter wheat is considered “better.”) The researchers grow both kinds under similar conditions and measure stalk heights, in inches, as follows. Which kind is better?

EXAMPLE 6.5 Means, Medians, and Modes d Compare two sets of data using their means. 9Growth of Wheat. Slide 23Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Note that it is difficult to analyze the data at a glance because the numbers are close together. We need a way to compare the two groups. Let’s compute the mean of each set of data.

EXAMPLE 6.5 Means, Medians, and Modes d Compare two sets of data using their means. 9Growth of Wheat. Slide 24Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE 6.5 Means, Medians, and Modes d Compare two sets of data using their means. 9Growth of Wheat. Slide 25Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. We see that the mean stalk height of wheat B is less than that of wheat A. Thus, wheat B is “better.”