Central Tendency

and Box Plots

Centers

Central Tendency

Centers

Grades

Your math grades on the last few tests are:

94, 92, 95, 93, 90, and 911. What is your average?

2. What will your average be if you make a zero on the next test?

3. How many 100s will it take to bring your grade back up to an A?

4. Which measure of central tendency would you want to use to represent your grades if you did make a zero on the next test?

Grades

1. 93

2. 79

3. Seven

4. The median would cross offthe zero immediately andwould be the best choice torepresent your grades sincethere is no mode.

Summer JobsFast food restaurants are often competing to get good part time help. One restaurant has jobs paying the following hourly wages: $5.85, $6.00, $6.00, $6.25, $6.50, $6.75, $7.50, and $18.50

1. Which method of central tendency makes the pay lookbetter to people who are looking for a job? Why?

2. Does this method give an accurate representation of thepay? Why or why not?

3. Which method should be used to represent the payaccurately?

4. Calculate the mean, median, and mode and discuss theadvantages and disadvantages of using each method.

Summer Jobs

1. The mean since it includes the outlier.

2. No. There is only one job that pays a much higheramount. Using this amount in the representation ofthe pay makes the pay seem higher than it really is.

3. Median because the outlier gets crossed offimmediately.

4. The mean pay is $7.92, which includes the outlier.

The median pay is $6.38, which excludes the outlier.

The mode pay is $6.00, but only occurs twice.

Bicycle ShopA bicycle shop is trying to restock tires for the summer. It is your job to decide how many of each tire to order. You may only buy one tire size, and you have the previous summer sales to help you decide.

Tire Size Number Sold

18”

20”

24”

1 99

27” 9

Calculate the mean, median, and mode and discuss the advantages and disadvantages of using each to reorder tires.

Bicycle Shop

Mean: 24.4Median: 24Mode: 20, 24, 27 (essentially there isn't one because that only leaves the 18" tire not listed.)

The mean and median show that ordering the 24 inch tire is the best idea. However, it looks like the 20 inch and 27 inch tire is just as popular as the 24 inch. Since we can only order one tire size, I would order the 24 inch.

Phone Bill

Your dad tells you that you can have your own phone if you pay the bill. He shows you a list of the cost for all of the calls that you have made during the past several months.

$12, $12, $16, $19, $17, $30, $52

1. Calculate the mean, median, and mode anddiscuss the advantages and disadvantages ofusing each.

2. Which method of central tendency bestrepresents the data?

Phone Bill

1. Mean: $22.57

Median: $17

Mode: $12

2. The median is the best representationbecause $17 is around the center of the data.The mode only shows the low end and the meanincludes the outlier.

Band Practice

You need a place for your band to practice, and your mom says that you can use the garage if your band pays $100 each month towards the electricity. You and your band make a list of the money you have made over the last year: $100, $0, $0, $150, $0, $80, $90, $800, $75, $0, $200, $200.1. Calculate the mean, median, and mode and

discuss the advantages and disadvantages of usingeach to represent the amount your band makesper month.

2. Can your band afford the electricity each month?

Band Practice

1. Mean $141.25

Median $85.00

Mode $0

If you use the mean, you are including the $800 that is not an amount that your band can consistently make.The median is a good representation because it does not include the $800, but does include the money that you made all of the other months. The mode does not include any money that was made except for the most common months.

2. No. You cannot depend on the $800 outlier.

Box Plots

Centers

Pick a Number

1. What percent of students chose a number between 15 and 40?

2. What percent of students chose a number between 5 and 40?

3. What percent of students chose a number below 15?

4. How many students chose a number between 5 and 30?

5. How many students chose a number above 40?

Pick a Number

1. 50%

2. 75%

3. 25%

4. 10 students

5. 5 students

Snow Skiing ResortsThe following box plots show the annual snow fall amounts for the last fifty years for two resorts.

1. Based on the medians, which resort has more snowfall annually?2. Based on record high and record low, which resort has a more consistent snowfall?3. Which resort has a better chance of getting 300 inches of snow for the year? 4. What is the interquartile range of each box plot?

Snow Skiing Resorts

1. Mad Mountain

2. Powder Valley

3. Mad Mountain

4. Powder Valley 125 inches

Mad Mountain 200 inches

Movie ReviewsRatings by 20 movie critics.

1. Which movie received the highest review?2. Which movie got the most low reviews? How do you know?3. Why are movies B, C, and D missing part of the box plot?4. Which movie would you want to go see? Why?

Movie Reviews

1. Movie B

2. Movie A because 25% of the reviews were below 5.

3. Movie B: 25% of the reviews were 6s

Movie C: 25% of the reviews were 8s

Movie D: 25% of the reviews were 6s

4. Movie B because 75% of the reviews were between 6 and 8, but 25% of the reviews were between 8 and 9.

Box Plot Practice

above? Use the box plot above to answer the questions below.

1.2.

3.

4. What is the interquartile range?

Box Plots Practice

1. A

2. D

3. B

4. 4

1. Which class do you think was most successful on the quiz? Why?

2. Which class had a larger percentage of scores below 80?

3. Which class had a larger percentage of scores above 80?

4. The middle 50% of third period made between what scores?

Quiz Scores

Quiz Scores

1. Second

2. Third

3. Second

4. 75 and 80

Mean Absolute Deviation

Centers

Grades

Find the mean absolute deviation for the grades of six students in class A and class B listed below and tell which class is more consistent based on the MAD.

Class A Class B

85, 92, 88, 80, 91, 20 85, 92, 88, 80, 91, 74

Grades

MAD for Class A is 18.7 (rounded to the nearest tenth)

MAD for Class B is 5.3 (rounded to the nearest tenth)

Class B is more consistent based on the MAD because the MAD is lower.

NBA Players

Below are the number of points scored over the last five years for NBA players Kobe Bryant and LeBron James:

Kobe Bryant: {2201, 2323, 2430, 2832, 1819} LeBron James: {2304, 2250, 2132, 2478, 2176}

1. Find the mean of both data sets. Based on the means, who is the better scorer per year?

2. In the financial climate of the NBA, teams like consistency from their players so that they will be able to more accurately measure expectations. Based on each player’s mean absolute deviation from the data above, which player is more consistent?

NBA Players

1. Kobe Bryant’s mean is 2321LeBron James’ mean is 2268Based on each player’s mean, LeBron James is the better scorer.

2. Kobe Bryant’s MAD is 248.8LeBron James’ MAD is 98.4Based on the MAD of each player, LeBron is the more consistent scorer.

Video Games

Game Emma Sara1 30 152 20 253 10 204 20 255 20 15

Emma and Sara play five games on a handheld

video game and record their scores in the table

below. Which girl had the greater mean deviation for

her scores and what does that mean?

Video Games

Emma’s MAD is 4.

Sara’s MAD is 4.

Neither girl had a greater MAD.

They both score on average four points away from their own average score. They both have the same consistency rate.

Baseball Batting Averages

Year Chipper Jones Alex Rodriguez

2004 .248 .287

2005 .296 .322

2006 .325 .290

2007 .337 .314

2008 .364 .302

Consider the batting averages per year for Chipper Jones and Alex Rodriguez.

A)What is the mean absolute deviation for Chipper Jones' batting averages?

B)What is the mean absolute deviation for Alex Rodriguez's batting averages?

C) Which player has the higher mean batting average (not mean absolute deviation)?

D) Based on the mean absolute deviations from A and B above, who has been the more consistent hitter?

E) Based on the means from C above, who has been the better hitter?

Baseball Batting Averages

A) .034

B) .012

C) Jones

D) Rodriquez is more consistent

E) Jones

Tip MoneyHourly Tips

Greg Trent

$15 $20

$24 $22

$26 $18

$18 $18

$17 $17

1. Greg’s mean tip money. ____________

2. Trent’s mean tip money. ____________

3. Combined mean tip money. ____________4. Mean absolute deviation of combined tip money. _____________5. Mean absolute deviation of Trent’s tip money. _______________6. Mean absolute deviation of Greg’s tip money. _____________7. Who’s mean absolute deviation is closer to the deviation of the combined tip money? ______8. Is a mean more relevant if the mean absolute deviation is smaller or larger?

Tip Money

1. $20

2. $19

3. $19.50

4. $2.80

5. $1.60

6. $4.00

7. The MAD is 1.2 for each

8. Smaller