Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 9 Statistics and Probability

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.1 Reading Pictographs, Bar Graphs, Histograms, and Line Graphs

Martin-Gay, Basic Mathematics, 4e 33 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Reading Pictographs A pictograph is a graph in which pictures or symbols are used. This type of graph contains a key that explains the meaning of the symbol used. Advantage – comparisons can easily be made Disadvantage – hard to tell what fractional part of a symbol is shown

Martin-Gay, Basic Mathematics, 4e 44 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The following pictograph shows the approximate number of spaceflights by various countries or space consortia for lunar or planetary explorations from 1957 to the present day. Use the graph to answer the questions. continued

Martin-Gay, Basic Mathematics, 4e 55 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued a. Approximate the number of space flights by the United States. The United States corresponds to 12 ½ symbols, and each symbol represents 12 ½ · 7 = 87.5 ≈ 87 spaceflights for lunar and planetary exploration. b. Approximate how many more spaceflights were undertaken by the USSR/Russia than by the United States The USSR/Russian shows 16 symbols, or 3 1 /2 more than the U.S. This means that the USSR/Russia undertook 3 ½ · 7 = 24.5 ≈ 24 more spaceflights than the United States.

Martin-Gay, Basic Mathematics, 4e 66 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Reading and Constructing Bar Graphs A bar graph can appear with vertical bars or horizontal bars. Advantage – the scale is usually included for great accuracy.

Martin-Gay, Basic Mathematics, 4e 77 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The following bar graphs shows the number of endangered species in the United States in Use the graph to answer the questions. continued

Martin-Gay, Basic Mathematics, 4e 88 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued a. Approximate the number of endangered species that are clams. We go to the top of the bar that represents clams. There are approximately 62 clam species that are endangered. b. Which category has the most endangered species? The most endangered species is represented by the tallest bar. The tallest bars correspond to birds and fish.

Martin-Gay, Basic Mathematics, 4e 99 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Reading and Constructing Histograms A histogram is a special bar graph. The with of each bar represents a range of numbers called a class interval. The height of each bar corresponds to how many times a number in the class interval occurs and is called class frequency. The bars in a histogram lie side by side with no space between them.

Martin-Gay, Basic Mathematics, 4e 10 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Reading Line Graphs Another common way to display information with a graph is by using a line graph. Advantage – it can be used to visualize relationships between two quantities. It can also show a change over time.

Martin-Gay, Basic Mathematics, 4e 11 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The following line graph shows the average daily temperature for each month for Omaha, Nebraska. Use the graph to answer the questions. continued

Martin-Gay, Basic Mathematics, 4e 12 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued a. During which month is the average daily temperature the highest? This corresponds to the highest point, which is July. b. During what month, from July through December, is the average daily temperature During the month of September, the average daily temperature was c. During what months is the average daily temperature less than These months were January, February, and December.

Martin-Gay, Basic Mathematics, 4e 13 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Video  Video for 9.1

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.2 Reading Circle Graphs

Martin-Gay, Basic Mathematics, 4e 15 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the ratio of baseball players to basketball players.

Martin-Gay, Basic Mathematics, 4e 16 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The following graph shows the percent of visitors to the U.S. in a recent year by various regions. Use the circle graph to determine the percent of visitors who came to the U.S. from Mexico and Canada. 12.3% % = 49.8%

Martin-Gay, Basic Mathematics, 4e 17 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The U.S. Department of Commerce forecasts 61,000,000 international visitors to the U.S. in Estimate the number of tourist that might be from Europe. amount = percent · base amount = 0.20 · 61,000,000 = 0.20(61,000,000) = 12,200,000

Martin-Gay, Basic Mathematics, 4e 18 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The following table shows the percentage of U.S. armed force personnel that were in each branch of service in (Source: U.S. Department of Defense) Draw a circle graph showing this data. Branch of ServicePercent Army38 Navy23 Marine Corps14 Air Force22 Coast Guard3 continued

Martin-Gay, Basic Mathematics, 4e 19 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued First we find the number of degrees in each sector. SectorDegrees in Each Sector Army Navy Marine Corps Air Force Coast Guard continued

Martin-Gay, Basic Mathematics, 4e 20 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued Next we draw a circle, mark its center and draw a line from the center to the circle itself. We then use a protractor to construct the sections. A protractor measures the number of degrees in an angle. It makes no difference which sector you draw first. continued

Martin-Gay, Basic Mathematics, 4e 21 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued To construct the “Navy” sector, we follow the same procedure, except we line up 0 degrees with the second line. continued

Martin-Gay, Basic Mathematics, 4e 22 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued We continue until the graph is complete.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.3 Mean, Median, and Mode

Martin-Gay, Basic Mathematics, 4e 24 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding the Mean The mean (average) of a set of number items is the sum of the items divided by the number of items

Martin-Gay, Basic Mathematics, 4e 25 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the mean of the following numbers: 42, 35, 36, 40, 50.

Martin-Gay, Basic Mathematics, 4e 26 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example The following grades were earned by a student during one semester. Find the student’s grade point average. CourseGradeCredit Hours College mathematicsA3 World HistoryB3 EnglishB3 PEC1 PsychologyD2 continued

Martin-Gay, Basic Mathematics, 4e 27 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example We use the point values of grades: A: 4, B: 3, C: 2, D: 1, F: 0 Now to find the grade point average, we multiply the number of credit hours for each course by the point value of each grade. The grade point average is the sum of these products divided by the sum of the credit hours. continued

Martin-Gay, Basic Mathematics, 4e 28 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. continued CourseGradePoint Value of Grade Credit Hours Point Value Credit Hours College Mathematics A4312 World HistoryB339 EnglishB339 PEC212 PsychologyD122 Totals1234 Grade point average =

Martin-Gay, Basic Mathematics, 4e 29 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding the Median The median of a set of numbers in numerical order is the middle number. If the number of items is odd, the median is the middle number. If the number of items is even, the median is the mean of the middle two middle numbers.

Martin-Gay, Basic Mathematics, 4e 30 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the median of the following numbers: 42, 35, 36, 40, 50. Place the numbers in numerical order. Median = 40

Martin-Gay, Basic Mathematics, 4e 31 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Finding the Mode The mode of a set of numbers is the number that occurs most often. (It is possible for a set of numbers to have more than one mode or to have no mode at all.

Martin-Gay, Basic Mathematics, 4e 32 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Find the mode of the following numbers: 37, 35, 31, 40, 37, 26, 35, 50. There are two numbers that occur most often. They are 35 and 37. Mode = 35 and 37

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. 9.4 Counting and Introduction to Probability

Martin-Gay, Basic Mathematics, 4e 34 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Using a Tree Diagram In our daily lives, we often talk about the likelihood or probability of a given result occurring. For example: The chance of snow is 70 percent. What are the odds that Argentina will win the World Cup? What is the probability that you will finish your report today? One way to picture outcomes is to draw a tree diagram.

Martin-Gay, Basic Mathematics, 4e 35 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Draw a tree diagram for tossing a coin twice. Then use the diagram to find the number of possible outcomes. There are 4 possible outcomes when tossing a coin twice.

Martin-Gay, Basic Mathematics, 4e 36 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example Draw a tree diagram for an experiment consisting of rolling a die and then tossing a coin. Find the number of possible outcomes. There are 12 possible outcomes.

Martin-Gay, Basic Mathematics, 4e 37 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. The Probability of an Event

Martin-Gay, Basic Mathematics, 4e 38 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example If a coin is tossed twice, find the probability of tossing tails of the first toss and then heads on the second toss. (T, H) Probability = The probability of tossing tails then heads is ¼. Possible outcomes: H, H, H, T T, H T, T Number of ways the event can occur Number of possible outcomes

Martin-Gay, Basic Mathematics, 4e 39 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Example If a die is rolled one time, find the probability of rolling a 2 or a 5. Probability of a 2 or a 5 = Possible outcomes: 1, 2, 3, 4, 5, 6 Number of ways the event can occur Number of possible outcomes

Martin-Gay, Basic Mathematics, 4e 40 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Video for 9.4  Watch video

Martin-Gay, Basic Mathematics, 4e 41 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Exercises in text

Martin-Gay, Basic Mathematics, 4e 42 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. Group Activity

Martin-Gay, Basic Mathematics, 4e 43 Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall. HOMEWORK  Is already posted on MyMathLab  Next class we will prep for the test, take the test, then start chapter 10.