Multi-Part Lesson 1

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Measures of Central TendencyAPART B C D E F

Multi-Part Lesson 1

650 Analyze Data and Graphs

Median, Mode, and Range HURRICANES The table

shows the number of Atlantic

hurricanes in different years.

1. Order the data from least to

greatest. Which piece of data

is in the middle of this list?

2. Compare this number to the

mean of the data.

A data set can also be described by its median or its mode. The mean,

median, and mode are called measures of central tendency because

they describe the center of a set of data.

Median and Mode

The median is the middle number of the ordered data or the mean of the middle two numbers.

The mode is the number or numbers that occur most often.

Find the Median and the Mode

MONKEYS The table shows the Number of Monkeys

28 36 18 25 12 44 18 42 34 16 30

number of monkeys at eleven

different zoos. Find the median

and mode of the data.

Order the data from least to greatest.

Median 12, 16, 18, 18, 25, 28, 30, 34, 36, 42, 44 28 is in the middle.

Mode 12, 16, 18, 18, 25, 28, 30, 34, 36, 42, 44 18 occurs most often.

The median is 28 monkeys. The mode is 18 monkeys.

a. BUILDINGS The list shows the number of stories in the

11 tallest buildings in Springfield. Find the median and

mode of the data.

40, 38, 40, 37, 33, 30, 20, 24, 21, 17, 19

Main IdeaFind and interpret the median, mode, and range of a set of data.

Vocabularymeasures of central

tendencymedianmoderange

Vm

Atlantic Hurricanes

5 15 9 7 4 9 8

The range of a set of data is the difference between the greatest and

the least values of the set. A large range indicates that the data are

spread out. A small range indicates that the data are close in value.

Find the Range

COINS The table gives

the weights and

diameters of the coins

used in the U.S. Find

the range of the

weights. Then write

a sentence that

describes how the

data vary.

The greatest weight is 5.670 grams, and the least weight is

2.268 grams. So, the range is 5.670 - 2.268 or 3.402. The range

is relatively large, so the data are spread out.

b. COINS Find the range of the diameters of the coins above. Then

write a sentence that describes how the data vary.

WEATHER Find the mean, median,

mode, and range of the temperatures

displayed in the graph.

Mean 64.4 + 71.2 + 55.8 + 58.2

__ 4

= 249.6 _

4 or 62.4°

Median 55.8, 58.2, 64.4, 71.2

58.2 + 64.4

_ 2 = 122.6

_ 2

= 61.3°

Mode There is no mode.

Range 71.2 - 55.8 = 15.4°

c. BACKPACKS Find the mean, Cost of Backpacks ($)

16.78 48.75 31.42 18.38

22.89 51.25 28.54 26.79

median, mode, and range

of the costs in the table.

Coin Weight (g) Diameter (mm)

dime 2.268 17.91 nickel 5.000 21.21 penny 2.500 19.05 quarter 5.670 24.26

United States Coins

Wed.Tue.Mon.Sun.

6065

55

050

7570

Tem

pera

ture

(°F)

Day

64.4

71.2

55.8 58.2

Daily High Temperature

There are an even number of data values. So, to find the median, find the mean ofthe two middle numbers.

Everyday Use

Range in music, all the notes between the high and low notes, as with a singer with a wide range

Math Use

Range the difference between the greatest number and least number in a set of data

Range The range of a set of data describes how much the data vary. It is called a measure of variability.

Lesson 1D Measures of Central Tendency 651

Find the median, mode, and range for each set of data.Examples 1 and 2

1. points scored by football team: 15, 20, 23, 13, 17, 21, 17

2. monthly spending: $46, $62, $63, $57, $50, $42, $56, $40

Find the mean, median, mode, and range of the data represented.Example 3

3. 4.Cost of CDs ($)

11.95 12.89 19.99

19.99 12.59 18.49

20102009200820072006

3020

010M

embe

rs

4050

Year

21 19

40

26

14

Debate Club Membership

= Step-by-Step Solutions begin on page R1. Extra Practice begins on page EP2.

Find the median, mode, and range for each set of data.Examples 1 and 2

5. age of employees: 23, 22, 15, 36, 44

6. minutes spent on homework: 18, 20, 22, 11, 19, 18, 18

77 math test scores: 97, 85, 92, 86

8. height of trees in feet: 23, 27, 24, 26, 26, 24, 26, 24

ANALYZE DISPLAYS Find the mean, median, mode, and range of the data

represented. Round to the nearest tenth if necessary.

Example 3

9. 10.Average Speeds (mph)

40 52 44 46

52 40 44 50

41 44 44 50

Test Grades

100 77 80 65

87 85 85 82

100 97 95 75

11. 12.

1 2 3 4 5 6 7

2

4

6

8

Laps

Sw

am

10

1214

16

Day

0

Emilia’s Swimming Schedule

Num

ber o

f Job

s

05

1015202530

Month321 4 5 6

813 12

26

1510

Yardwork Jobs

B 1313 ANALYZE TABLES A Louisville Daily High Temperatures (°F)

Louisville Lexington

75 50 80 72 80 73 75 74

70 84 70 71 76 76

newspaper claims that during seven

days, the high temperature in

Lexington was typically 6° warmer

than the high temperature in

Louisville. What measure was used to

make this claim? Justify your answer.

14. MATH IN THE MEDIA Use the Internet to find the high temperatures for

each of the last seven days in a city near you. Then find the median high

temperature.

15. GRAPHIC NOVEL Refer to the graphic novel frame below for Exercises a–b.

Let’s check

other measures

to really see

which team is

better.

a. Find the median, mode, and range for each team’s wins.

b. Which team had the better record? Justify your response.

C 16. CHALLENGE The ticket prices for a concert series were $12, $37, $45,

$18, $8, $25, and $18. What was the ticket price of the eighth and

final concert in this series if the set of 8 prices had a mean of $23,

a mode of $18, a median of $19.50, and a range of $37?

17. REASONING One evening at a local pizzeria, the following number of

toppings were ordered on each large pizza.

3, 0, 1, 1, 2, 5, 4, 3, 1, 0, 0, 1, 1, 2, 2, 3, 6, 4, 3, 2, 0, 2, 1, 3

Determine whether each statement is true or false. Explain your

reasoning.

a. The greatest number of people ordered a pizza with 1 topping.

b. Half the customers ordered pizzas with 3 or more toppings,

and half the customers ordered pizzas with less than 3 toppings.

18. E WRITE MATH In the data set {3, 7, 4, 2, 31, 5, 4}, which measure

best describes the set of data: mean, median, or mode? Explain your

reasoning.

Lesson 1D Measures of Central Tendency 653

Test PracticeT

23. CELL PHONE Find the mean number of cell phone minutes Tucker

used each month this year. (Lesson 1B)

Month Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.

Minutes Used 49 65 20 37 55 68 75 50 24 37 42 30

24. Malcolm’s and Leo’s last four math test scores are shown in the graphs

below. Write a sentence comparing the mean scores of the students. (Lesson 1B)

19. EXTENDED The Quest

Year Number of Concerts

2003 142

2004 142

2005 136

2006 136

2007 124

2008 138

2009 136

2010 150

RESPONSE The

table shows the

number of concerts

performed by The

Quest.

Part A What is the difference between the median number of concerts and the mode number of concerts for 2003–2010?

Part B Write a sentence describing the data.

20. The lengths of the 5 long jumps at track

practice were 14.5 feet, 13.7 feet, 14.1 feet,

14.9 feet, and 13.8 feet. What would the

sixth length have to be to have a mean

length of 14.1 feet?

A. 14.8 feet C. 13.6 feet

B. 14.1 feet D. 12.9 feet

21. SHORT RESPONSE The prices of some

dinners at the Town Diner are shown in

the table.

Dinner Price($)

Turkey 9.90

Cheeseburger 6.75

Chicken Salad 5.29

Spaghetti 8.15

What is the range of prices in dollars for

the meals?

22. The table shows the number of schools

in 12 different counties. What is the

median of the data?

Number of Schools

4 3 6 10 3 148 5 7 11 7 8

F. 4 H. 7

G. 6 I. 8

Malcolm’s Test Scores

1 2 3 4

Test

Scor

e (p

erce

nt)

0

20

40

60

80

100 78%88% 90%

100%Leo’s Test Scores

1 2 3 4

Test

Scor

e (p

erce

nt)

0

20

40

60

80

100 80% 78%92% 94%