5 th Grade Math Docent Program. Session 8

Transcription

1 5 th Grade Math Docent Program Session 8 Today s Topic: Averages: Mean, Median, Mode Name: Session 8 Practice Problems Page 8-1

2 Date: Session 8 Practice Problems Page 8-2

3 Session 8 Parent Presentation In today s session we will review and solve word problems about different types of averages. Averages: Mean, Median, and Mode Mean, median and mode are types of averages and each works best in different types of situations. The mean is the most common average. Knowing all three is a good way to know what kind of data you're looking at. Why do we study mean, median, and mode? How is it going to help us later in life? To answer these questions, let s look at a few demonstration problems on mean, median, and mode Mean and Median Demonstration Problem Suppose you are an adult looking for a job. You interview with a small company that has ten employees, and the interviewer tells you that the average (mean) salary is $200 per day. Wow, that s a lot of money! But that s not what you would be making. For this particular company, you would make half of that. Each employee makes $100 per day, except for the owner, who makes $1,100 per day. What? How do they get $200 for average then? To get the average (mean): Nine employees make $100, and the owner makes $1100. Add up the salaries for all ten employees, (9x$100) + $1100 = $2000. Divide by the total number of employees, ten, and we have $2000/10 = $200. Because the owner makes so much more than everyone else, her salary pulls the average up. A better question to ask the interviewer is, What is the Median salary? The median is the number in the middle, when the numbers are listed in order from smallest to largest. To get the median: Let s look at those salaries again. To find the median salary, we look at the salaries in order: 100, 100, 100, 100, 100, 100, 100, 100, 100, This is an even number of salaries, so we look at the middle two. Since they are both 100, the median is $100. That s much better at telling you how much you ll make if you accept the job! Answer: The median is $100 per day. The mean is $200 per day. Session 8 Practice Problems Page 8-3

4 Mode Demonstration Problem Sometimes the median doesn t always give you the best information either. Suppose you interview with a company that has 10 general employees, 7 assistants, 3 managers, and 1 owner. For this company, the mean salary is $400, and median is also $400. But you are applying for the position of general employee, whose starting salary is $100! Why are the mean and median so far away? Well, the 10 general employees each make $100. The 7 assistants each make $400, the 3 managers each make $900, and the owner makes $1900. To find the mean salary: 1. Add up the salaries: (10 x $100) + (7 x $400) + (3 x $900) + $1900 = $ Divide the total by the number of employees: $8400/21 = $400 The mean salary is: $400. To find the median salary: 1. List them in order: 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 400, 400, 400, 400, 400, 400, 400, 900, 900, 900, Now which one is in the middle? 400. The median salary is $400. To find the mode salary: The mode is the type of average you want to know in this situation. The mode is the number that occurs most frequently. In this salary example, the mode is $100 because that number occurs ten times, which is more than any other number occurs. Answer: The mean salary is $400, the median is also $400 per day, and the mode is $100. Session 8 Practice Problems Page 8-4

5 Session 8 Student Practice Problems Note: You may use your calculators for routine computations. Problem #1: Jamaican Bobsled Team In order for the Jamaican bobsled team to make it to the Olympics, the average (mean) run time of their last 10 races must be 10.0 seconds or less. Here is a list of their last 10 run times: 9.9 seconds, 12.5 seconds, 10.0 seconds, 8.1 seconds, 10.5 seconds, 12.3 seconds, 11.2 seconds, 9.5 seconds, 8.0 seconds, 8.0 seconds. Did the Jamaican Bobsled team get to go to the Olympics? Please explain your answer. Session 8 Practice Problems Page 8-5

6 Problem #2: What s the best deal? Meg went to Mr. Math s candy story. Mr. Math is having a clearance sale on all leftover gummy candy. His store has: 100 black gummy spiders 50 yellow gummy bears 10 green gummy bears 40 red gummy bears 25 sour grape gummy worms 20 sour apple gummy worms 50 rainbow gummy worms Mr. Math says that she could buy the median number or mode number of gummy candies for $1.00. Which should she choose to get the most candy for $1.00? Please explain your answer. Session 8 Practice Problems Page 8-6

7 Problem #3: The Grinch buys a Who-house The Grinch wants to buy a house in Whoville. Here is a list of the home prices in Whoville that are for sale: $2000, $5000, $100,000, $3500, $3000, $2800, $1200, $2100, $1500, $1200 Should the Grinch shop for the mean price or the median price of a Who-house? Please explain your answer. Hint: The Grinch is very stingy. Session 8 Practice Problems Page 8-7

8 Problem #4: Girls Basketball Finals Coach Trish says that the players with the top 3 average (mean) scores of the season will be on the Girls Basketball Finals team. Twelve games were played this season. Sheri missed half the season due to a foot injury. Carla missed the last game because she was at the dentist. All the other girls played every game of the season. Here are the players game scores for the season. Jennifer: 18, 10, 20, 22, 6, 12, 14, 15, 20, 25, 20, 18 Carla: 28, 10, 6, 22, 26, 10, 10, 28, 28, 32, 30 Lindsay: 30, 32, 28, 4, 10, 12, 16, 0, 6, 36, 10, 8 Sheri: 36, 30, 30, 32, 28, 32 Which girls made it to the finals? Please explain your answer. Session 8 Practice Problems Page 8-8

9 Problem #5: Magic Averages The magician said, "The average (mean) of seven numbers is 49. If 1 is added to the first number, 2 is added to the second number, 3 is added to the third number and so on up to the seventh number", what is the new average? Session 8 Practice Problems Page 8-9

10 Problem #6: Tips at Sweet Tooth Kate has a part-time job waitressing at Sweet Tooth, the ice cream parlor in her hometown. She works Friday, Saturday, and Sunday from 4-10 p.m. This weekend was very busy at the ice cream parlor, on Friday she waited on 40 tables, on Saturday she waited on 60 tables, and on Sunday she waited on 44 tables. Her average customer order total was $ Customers really like Kate, so they regularly leave her a 20% tip. What is the amount of money Kate collected in tips this week? (Remember Kate only gets to keep the tip!) Hint: A 10% tip on ten dollars is $1.00. Session 8 Practice Problems Page 8-10

11 Problem #7: Mean Jellybeans Mr. Cal Q. Later has pulled out a bag of jellybeans. As he walks around the room, he places a few jellybeans on everyone's desk everyone s, that is, except Leo's. On Leo's desk he places the bag with the remaining jellybeans. Here are the numbers: Mr. Later tells the students that Leo's jellybeans are all that remain in his bag. If they can figure out how many are in the bag, each of them will get to eat the average number of jellybeans, which is 10. Harumi raises her hand and asks which average he is referring to: the mean, median, or mode? Mr. Later says they have enough information to figure that out themselves. How many jellybeans are in the bag on Leo's desk? Explain your answer. Session 8 Practice Problems Page 8-11

12 Problem #8: Batting Averages In May 1999, two National League baseball players, Joe McEwing of the St. Louis Cardinals and Mike Lieberthal of the Philadelphia Phillies, each had the batting averages shown below: Player Bats Hits Batting Average M. Lieberthal J. McEwing Suppose McEwing then batted.800 (4 hits in 5 at bats), and Lieberthal was perfect (3 hits in 3 at bats). Which player now has the higher batting average? Are you surprised? Please explain your answer. Hint: The Batting Average = Number of hits Number of at bats (rounded to the nearest thousandth) Session 8 Practice Problems Page 8-12