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7.3 Data Interpretation 1 Objective A. Mean, Median and Mode Mean (Average) The mean of a set of numbers is the sum of the numbers divided by the number of addends. Example 1. A student received scores of 72, 87, and 54. Find the average of the scores. Solution: Add the scores, then divide by 3. 72 +87 +54 = 213, Then: 213 3 =71. Answer: The students average is 71. Lori has 4 math tests with scores of 76, 85, 92, and 91. Find the average of all four tests. Your Turn Problem #1 Answer: Lori’s average is 86.

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7.3 Data Interpretation 2 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 unit 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 Grade Point Average Example 2. Kelly earned the following grades for one semester. What was her grade point average? (Round to the tenths place.) CourseGrade# of Units MathematicsA4 HistoryB4 EnglishC3 SpanishB3 BiologyC4 51 total 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 Multiplying grade point values by the number of units for each course The total number of units taken is: 4 + 4 + 3 + 3 + 4 = 18 Now, divide 51 by 18. Kelly’s grade point average was 2.8. Some classes carry more weight then others. Her A in math could count as 4-A’s. Rather than list them all out, we will multiply and then add before dividing.

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7.3 Data Interpretation 3 Your Turn Problem #2 Answer: Sonya’s G.P.A. is 3.4. CourseGrade# of Units MathA4 BiologyB5 P.E.A1 MusicB4 Sonya earned the following grades for one semester. What was her grade point average? (Round to the tenths place.)

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7.3 Data Interpretation 4 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. Median Example 3. 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 median is the average of the two middle numbers. The mass, in grams, of five eggs are as follows: 15 g, 19 g, 19 g, 14 g, and 18 g. Find median mass of the five eggs. Your Turn Problem #3 Answer: 18 g The two middle numbers are 72,000 and 81,000

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7.3 Data Interpretation 5 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. Mode Example 4. Find the mode of these data. 23, 24, 27, 27, 18, 29 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. Solution: The number that occurs most often is 27. Answer 1. There is no mode. 2. The modes are 55 and 67. Your Turn Problem #4 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

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7.3 Data Interpretation 6 Objective B. To extract and interpret data from tables A table is often used to present data in rows and columns. The following table lists the nutrition information for five breakfast cereals. CerealFiberSaltSugarSaturated Fat Golden Grahams3g to 6 g1.25 g10 gless than 5 g Crispix< 3g1.25 g10 gless than 5 g Shredded Wheat6 g or more0.25 g less than 5 g Banana Nut Crunch6 g or more< 1.25 g< 10 gless than 5g Honey Nut Cheerios3 g to 6 g1.25 g10 gless than 5 g Example 5. a) Which cereal has the least amount of sugar? Answer: Shredded wheat has the least amount at 0.25 g b) Which cereal has the least amount of salt? Answer: Shredded wheat has the least amount at 0.25 g c) Which cereal has the greatest amount of fiber? Answer: Both Shredded Shredded Wheat and Banana Nut Crunch have the greatest amount of fiber. Next Slide

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7.3 Data Interpretation 7 Planet Average Distance From Sun (in miles) Diameter (in miles) Length of Planet’s Day in Earth Time (in days) Time of Revolution in Earth Time (in years) Mercury35,983,0003,03158.820.24 Venus67,237,7007,520224.590.62 Earth92,955,9007,9261.00 Mars141,634,8004,2211.031.88 Jupiter483,612,20088,8460.4111.86 Saturn888,184,00074,8980.4329.46 Uranus1,782,000,00031,7630.4584.01 Neptune2,794,000,00031,3290.66164.78 *Pluto3,666,000,0001,4236.41248.53 Planets: Use the following table, which list information about the planets. *Pluto is now called a dwarf planet. Your Turn Problem #5 a) Find the average distance from the Sun to Jupiter. b) How long is a day on Venus? c) Which planets have an average distance from the Sun that is greater that one billion miles? d) Which planets have a diameter that is less than 5000 mi? Answers a) 483,612,200 mi b) 224.59 earth days c) Uranus, Neptune, Pluto d) Mercury, Mars, Pluto

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7.3 Data Interpretation 8 Objective C: To extract and interpret data from bar graphs Source: Based on information from Olen.com and the Minnesota Attorney General's Office 0 5 10 15 20 25 30 35 40 Fat content (in grams, g) Food on the Move Example 6. a) Which item contains the most fat?Answer: Burger King’s Whopper b) Which item contains about 23 g of fat? Answer: KFC’s Original Chicken Sandwich Slice of Pizza Hut’s Pepperoni Pizza Burger King’s Whopper McDonald’s Big Mac Wendy’s Big Bacon Classic Subway’s Meatball Sandwich KFC’s Original Chicken Sandwich c) How much fat is in a subway meatball sandwich? Answer: 15 grams

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7.3 Data Interpretation 9 The following chart indicates the profit (in billions) for a “much too popular” coffee franchise. c) What is the percent decrease in profit from 2006 to 2007? (Hint: Use P, B, A, where B = original and A = amount of increase or decrease) a) How much did their annual profit increase by from 2002 to 2005? Your Turn Problem #6 b) Which year had the largest decrease in profit from the previous year? Answers a) 60 billion b) 2006; $30 billion decrease c) 37.5% decrease

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7.3 Data Interpretation 10 c) For which year was the water level the lowest? b) For which year was the water level the highest? Example 7. a) Between what two years was the increase in water level the greatest? Objective D: To extract and interpret data from line graphs Answer: 2000 Answer: 1970 and 1980 Answer: 2005

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7.3 Data Interpretation 11 Average Salary of Major league Baseball Players. The following graph shows the average salary of Major League baseball players over a recent 12 year period. Your Turn Problem #7 a) In which year was the average salary the highest? b) What was the difference in salary between the highest and the lowest salaries? c) In what year was the average salary about $1.2 million? Answers a) 2002 b) 1.6 billion c) 1996 Salary (in millions) Year

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7.3 Data Interpretation 12 The following circle graph shows the favorite breakfast foods for students. Favorite Breakfasts b. What percent of the students favorite breakfast food is eggs and pancakes? Example 8. a. What is the most popular item? Answer: Cereal Answer: 31% c. If there are 400 students, how many of them chose waffles as their favorite food? Objective E: To extract and interpret data from circle graphs Answer: 28 Next Slide

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7.3 Data Interpretation 13 Vacation Destinations Your Turn Problem #9 a) What percent of the people did not choose Hawaii for the place they would most like to visit? The circle graph shows where people would most like to visit are given in the list to the right. b) Out of 12,000 people, how many of them would most like to visit the Grand Canyon? Answer: a)42% b)1800 The End B.R. 6-19-08

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

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