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Median

27.04 0

616	Chapter 7 Graphs and Statistics

Solution

a. To ﬁnd the mean, we add the measurements and divide by the				3	4
				3.43
number of values, which is 8.				3.25		3.38
				3.48		8
	3.43 3.25 3.48 3.39 3.54 3.48 3.23 3.24						27.04
Mean				3.39		24

			8
		27.04		3.54		3		0

			In the numerator, do the addition.	3.48		2		4
				3.23				64
8
3.38			Do the division.	3.24				64

The mean is 3.38 cm.

b.To ﬁnd the median, we ﬁrst arrange the eight measurements in increasing order.

Smallest	3.23	3.24	3.25	3.39	3.43	3.48	3.48	3.54	Largest

Two middle measurements

Because there is an even number of measurements, the median is the average of the two middle values.

3.39 3.43 6.82 3.41 cm

2 2

c. Since the measurement 3.48 cm occurs most often (twice), it is the mode.

THINK IT THROUGH The Value of an Education

“Additional education makes workers more productive and enables them to increase their earnings.”

Virginia Governor, Mark R.Warner, 2004

As college costs increase, some people wonder if it is worth it to spend years working toward a degree when that same time could be spent earning money. The following median income data makes it clear that, over time, additional education is well worth the investment. Use the given facts to complete the bar graph.

Median Annual Earnings of Full-Time Workers (25 years and older) by Education

$70,000
$60,000
$50,000
$40,000
$30,000
$22,212
$20,000
$10,000
$0

Less than a		High	Some		Associate Bachelor’s Master’s
high school	school		college		degree		degree		degree
diploma	graduate
$8,603		$2,815		$4,745		$12,618		$13,035
more		more		more		more			more

Source: Bureau of Labor Statistics, Current Population Survey (2008)

ANSWERS TO SELF CHECKS

1.	$1,540	2. 120 miles per day	3. 2 incorrect answers 4. 2.75 5. 2	1	6. 80.5
7.	4 8.	mean: 5.11 oz; median:	5.00 oz; mode: 4.95 oz	2
7.	4 8.	mean: 5.11 oz; median:	5.00 oz; mode: 4.95 oz


	S E C T I O N				7.2		STUDY SET
		VOCABULARY


	Fill in the blanks.
1.			The		(average) of a set of values is the sum of
			the values divided by the number of values in the set.
2.			The			of a set of values written in increasing
			order is the middle value.
3.			The		of a set of values is the single value that
			occurs most often.
4.			The mean, median, and mode are three measures of
				tendency.

CONCEPTS

5.Fill in the blank. The mean of a set of values is given by the formula

Mean the sum of the values

6.Consider the following set of values written in increasing order:

a.Is there an even or an odd number of values?

b.What is the middle number of the list?

c.What is the median of the set of values?

7.Consider the following set of values written in increasing order:

a.Is there an even or odd number of values?

b.What are the middle numbers of the set of values?

c.Fill in the blanks:

Median 2 2

8. Consider the following set of values:

a.What value occurs the most often? How many times does it occur?

b.What is the mode of the set of values?

7.2 Mean, Median, and Mode

617

GUIDED PRACTICE

Find the mean of each set of values. See Example 1.

9.	3	4	7	7		8		11	16
10.	13		15	17		17		15	13
11.	5	9	12		35		37		45	60	77
12.	0	0	3	4		7		9	12
13.	15		7	12	19			27	17	19	35	20
14.	45		67	42		35		86	52	91	102
15.	4.2		3.6	7.1		5.9			8.2
16.	19.1		12.8		16.5			20.0

Find the median of each set of values. See Example 5.


17.	29		5		1		9	11				17		2
18.	20		4		3		2	9				8		1
19.	7	5	4		7			3			6	7		4		1
20.	0	0	3		4			0			0	3		4		5
21.	15.1		44.9					19.7				13.6				17.2
22.	22.4		22.1					50.5				22.3				22.2
23.	1			999					16			1			5
23.	100		1,000					15				3		8
24.	1		17			7				29			11
24.	30		30		30			30				30

Find the median of each set of values. See Example 6.

25.	8	10		16		63		6			7
26.	7	2		11		5		4		17
27.	39	1		50		41		51			47
28.	47	18		35			29			27	16
29.	1.8	1.7				2.0		9.0			2.1	2.3	2.1	2.0
30.	5.0	1.3				5.0		2.3			4.3	5.6	3.2	4.5
31.	1		11		13		2		3		7
31.	5	5		5			5	5			5
32.	1	2		7		11		13			29

	9	9		9		9		9			9

618	Chapter 7 Graphs and Statistics

Find the mode (if any) of each set of values. See Example 7.

33.	3	5		7		3		5		4	6		7	2			3	1		4
34.	12	12				17		17		12	13			17				12
35.	6			7		6		4			3			6				7
36.	0	3		0		2		7		0	6		0	3			4	2		0
37.	23.1			22.7			23.5			22.7				34.2			22.7
38.	21.6			19.3			1.3			19.3			1.6			9.3		2.6
39.	1		1		1		2		1	2		1			1		5		1
	2	3		3				2			5			2				3
40.	5	9		12			35	37			45			60

APPLICATIONS

41.SEMESTER GRADES Frank’s algebra grade is based on the average of four exams, which count equally. His grades are 75, 80, 90, and 85.

a.Find his average exam score.

b.If Frank’s professor decided to count the fourth exam double, what would Frank’s average be?

42.HURRICANES The table lists the number of major hurricanes to strike the mainland of the United States by decade. Find the average number per decade.

Round to the nearest one.

Decade	Number	Decade	Number

1901–1910	4	1951–1960	8
1911–1920	7	1961–1970	6
1921–1930	5	1971–1980	4
1931–1940	8	1981–1990	5
1941–1950	10	1991–2000	5

Source: National Hurricane Center

43.FLEET MILEAGE An insurance company’s sales force uses 37 cars. Last June, those cars logged a total of 98,790 miles.

a.On average, how many miles did each car travel that month?

b.Find the average number of miles driven daily for each car.

44.BUDGETS The Hinrichs family spent $519 on groceries last April.

a.On average, how much did they spend on groceries each day?

b.The Hinrichs family has ﬁve members. What is the average spent for groceries for one family member for one day?

45.CASH AWARDS A contest is to be part of a promotional kickoff for a new children’s cereal. The prizes to be awarded are shown.

a.How much money will be awarded in the promotion?

b.How many cash prizes will be awarded?

c.What is the average cash prize?

Coloring Contest

Grand prize: Disney World vacation plus $2,500

Four 1st place prizes of $500

Thirty-five 2nd place prizes of $150

Eighty-five 3rd place prizes of $25

46.SURVEYS Some students were asked to rate their college cafeteria food on a scale from 1 to 5. The responses are shown on the tally sheet. Find the average rating.

Poor		Fair		Excellent
1	2	3	4	5

47.CANDY BARS The prices (in cents) of the different types of candy bars sold in a drug store are: 50, 60, 50, 50, 70, 75, 50, 45, 50, 50, 60, 75, 60, 75, 100, 50, 80, 75, 100, 75.

a.Find the mean price of a candy bar.

b.Find the median price for a candy bar.

c.Find the mode of the prices of the candy bars.

48.COMPUTER SUPPLIES Several computer stores reported differing prices for toner cartridges for a laser printer (in dollars): 51, 55, 73, 75, 72, 70, 53, 59, 75.

a.Find the mean price of a toner cartridge.

b.Find the median price for a toner cartridge.

c.Find the mode of the prices for a toner cartridge.

49.TEMPERATURE CHANGES Temperatures were recorded at hourly intervals and listed in the table below. Find the average temperature of the period from midnight to 11:00 A.M.

Time	Temperature	Time	Temperature

12:00 A.M.	53	12:00 noon	71
1:00	54	1:00 P.M.	73
2:00	57	2:00	76
3:00	58	3:00	77
4:00	59	4:00	78
5:00	59	5:00	71
6:00	61	6:00	70
7:00	62	7:00	64
8:00	64	8:00	61
9:00	66	9:00	59
10:00	68	10:00	53
11:00	71	11:00	51

50.AVERAGE TEMPERATURES Find the average temperature for the 24-hour period shown in the table in Exercise 49.

For Exercises 51–54, ﬁnd the semester grade point average for a student that received the following grades. Round to the nearest hundredth, when necessary.

51.	Course	Grade	Credits

	MATH 210	C	5
	ACCOUNTING 175	A	3
	HEALTH 090	B	1
	JAPANESE 010	D	4

52.	Course	Grade	Credits

	NURSING 101	D	3
	READING 150	B	4
	PAINTING 175	A	2
	LATINO STUDIES 090	C	3

53.	Course	Grade	Credits

	PHOTOGRAPHY	D	3
	MATH 020	B	4
	CERAMICS 175	A	1
	ELECTRONICS 090	C	3
	SPANISH 130	B	5

	7.2 Mean, Median, and Mode			619

54.	Course	Grade	Credits

	ANTROPOLOGY 050	D	3
	STATISTICS 100	A	4
	ASTRONOMY 100	C	1
	FORESTRY 130	B	5
	CHOIR 130	C	1

55.EXAM AVERAGES Roberto received the same score on each of ﬁve exams, and his mean score is 85. Find his median score and the mode of his scores.

56.EXAM SCORES The scores on the ﬁrst exam of the students in a history class were 57, 59, 61, 63, 63, 63, 87, 89, 95, 99, and 100. Kia got a score of 70 and claims that “70 is better than average.” Which of the three measures of central tendency is she better than: the mean, the median, or the mode?

57.COMPARING GRADES A student received scores of 37, 53, and 78 on three quizzes. His sister received scores of 53, 57, and 58. Who had the better average? Whose grades were more consistent?

58.What is the average of all of the integers from 100 to 100, inclusive?

59.OCTUPLETS In December 1998, Nkem Chukwu gave birth to eight babies in Texas Children’s Hospital. Find the mean and the median of their birth weights listed below.

Ebuka (girl)	24 oz	Odera (girl)	11.2 oz
Chidi (girl)	27 oz	Ikem (boy)	17.5 oz
Echerem (girl)	28 oz	Jioke (boy)	28.5 oz
Chima (girl)	26 oz	Gorom (girl)	18 oz

60.COMPARISON SHOPPING A survey of grocery stores found the price of a 15-ounce box of Cheerios cereal ranging from $3.89 to $4.39, as shown below. What are the mean, median, and mode of the prices listed?

$4.29 $3.89 $4.29 $4.09 $4.24 $3.99

$3.98 $4.19 $4.19 $4.39 $3.97 $4.29

620Chapter 7 Graphs and Statistics

61.EARTHQUAKES The magnitudes of 2008’s major earthquakes are listed below. Find the mean (round to the nearest tenth) and the median.

Date	Location	Magnitude

Jan. 5	Queen Charlotte	6.6
	Islands Region
Jan. 10	Off the coast of	6.4
	Oregon
Feb. 20	Simeulue, Indonesia	7.4
Feb. 24	Nevada	6.0
Feb. 25	Kepulauan Mentawai	7.0
	Region, Indonesia
March 21	Xinjiang-Xizang	7.2
	Border Region
April 9	Loyalty Islands	7.3
May 12	China	7.9
June 13	Eastern Honshu,	6.9
	Japan
July 19	Honshu, Japan	7.0
Oct. 6	Kyrgyzstan	6.6
Oct. 11	Russia	6.3
Oct. 29	Pakistan	6.4
Nov. 16	Indonesia	7.3
Dec. 20	Japan	6.3

Source: Incorporated Research Institutions for Seismology

62.FUEL EFFICIENCY The ten most fuel-efﬁcient cars in 2009, based on manufacturer’s estimated city and highway average miles per gallon (mpg), are shown in the table below.

a.Find the mean, median, and mode of the city mileage.

b.Find the mean, median, and mode of the highway mileage.

Model	mpg city/hwy

Toyota Prius	50/49
Honda Civic Hybrid	40/45
Honda Insight	40/43
Ford Fusion Hybrid	41/36
Mercury Milan Hybrid	41/36
VW Jetta TDI	30/41
Nissan Altima Hybrid	35/33
Toyota Camry Hybrid	33/34
Toyota Yaris	29/36
Toyota Corolla	26/35

Source: edmonds.com

63.SPORT FISHING The report shown below lists the ﬁshing conditions at Pyramid Lake for a Saturday in January. Find the median and the mode of the weights of the striped bass caught at the lake.

Pyramid Lake—Some striped bass are biting but are on the small side. Striking jigs and plastic worms. Water is cold: 38°. Weights

of ﬁsh caught (lb): 6, 9, 4, 7, 4, 3, 3, 5, 6, 9, 4, 5, 8, 13, 4, 5, 4, 6, 9

64.NUTRITION Refer to the table below.

a.Find the mean number of calories in one serving of the meats shown.

b.Find the median.

c.Find the mode.

NUTRITIONAL COMPARISONS

Per 3.5 oz. serving of cooked meat

Species	Calories

Bison	143
Beef (Choice)	283
Beef (Select)	201
Pork	212
Chicken (Skinless)	190
Sockeye Salmon	216

Source: The National Bison Association

WRITING

65.Explain how to ﬁnd the mean, the median, and the mode of a set of values.

66.The mean, median, and mode are used to measure the central tendency of a set of values. What is meant by central tendency?

67.Which measure of central tendency, mean, median, or mode, do you think is the best for describing the salaries at a large company? Explain your reasoning.

68.When is the mode a better measure of central tendency than the mean or the median? Give an example and explain why.

REVIEW

Translate to a percent equation (or percent proportion) and then solve to ﬁnd the unknown number.

69.52 is what percent of 80?

70.What percent of 50 is 56?

71.6623% of what number is 28?

72.56.2 is 16 13% of what number?

73.5 is what percent of 8?

74.What number is 52% of 350?

75.Find 7 14% of 600.

76.12% of what number is 5,000?

7 values

Chapter 7 Summary and Review

STUDY SKILLS CHECKLIST

Know the Deﬁnitions

Before taking the test on Chapter 7, make sure that you have memorized the deﬁnitions of mean, median, and mode. Put a checkmark in the box if you can answer “yes” to the statement.

□I know that the mean of a set of values is often referred to as the average.

□I know that the mean of a set of values is given by the formula:

sum of the values Mean number of values

□I know that the median of a set of values is the middle value when they are arranged in increasing order.

□I know how to ﬁnd the median of a set of values if there is an odd number of values.

2 4 5 8 10 13 14

Median Middle value

□I know how to ﬁnd the median of a set of values if there is an even number of values.

2	4	5	8	10	13	14	16	8 values
			⎬ ⎭
	Median 8 10				9
				2

□I know that the mode of a set of values is the value that occurs most often.

□I know that a set of values may have one mode, or more than one mode.

2	8	5	8	10	8 14	mode: 8
2	8	5	8	2 8	2	two modes: 2, 8

C H A P T E R 7 SUMMARY AND REVIEW

S E C T I O N 7.1 Reading Graphs and Tables

DEFINITIONS AND CONCEPTS

To read a table and locate a speciﬁc fact in it, we ﬁnd the intersection of the correct row and column that contains the desired information.

EXAMPLES

SALARY SCHEDULES Find the annual salary for a teacher with a master’s degree plus 15 additional units of study who is beginning her 4th year of teaching.

Teacher Salary Schedule

	Step	BA	BA+15	BA+30	BA+45	MA	MA+15	MA+30

1		37,295	38,362	39,416	40,480	41,556	42,612	43,669

2		38,504	39,581	40,652	41,728	42,812	43,879	44,952

3		39,716	40,802	41,885	42,973	44,066	45,147	46,234

	4	40,926	42,021	43,120	44,220	45,321	46,417	47,514
	5	42,135	43,240	44,356	45,465	46,577	47,682	48,795

6		44,458	45,567	46,683	47,782	48,897	50,010	51,113

7		46,780	47,891	49,003	50,115	51,226	52,330	53,438

The annual salary is $46,417. It can be found by looking on the fourth row (labeled Step 4) in the 6th column (labeled MA + 15).

622		Chapter 7 Summary and Review

A bar graph presents data using vertical or	CANCER DEATHS Refer to the bar graph below. How many more
horizontal bars. A horizontal axis and vertical	deaths were caused by lung cancer than by colon cancer in the United
axis serve to frame the graph and they are	States in 2007?
scaled in units such as years, dollars, minutes,		U.S. Cancer Deaths, 2007
pounds, and percent.
		200,000
	deathsof
		150,000

	Number	100,000
		50,000

		0 Colon Breast Prostate Liver Kidney Lung
		Source: Lung Cancer Alliance
	From the graph, we see that there were about 160,000 deaths caused by
	lung cancer and about 50,000 deaths from colon cancer. To ﬁnd the
	difference, we subtract:
	160,000 – 50,000 = 110,000

There were about 110,000 more deaths caused by lung cancer than

deaths caused by colon cancer in the United States in 2007.

To compare sets of related data, groups of two

SEAT BELTS Refer to the double-bar graph below. How did the

(or three) bars can be shown. For double-bar or

percent of male high school students that rarely or never wore seat

triple-bar graphs, a key is used to explain the

belts change from 2001 to 2007?

meaning of each type of bar in a group.

Risk Behaviors in High School Students

2001

Year

Male

2007

Female

12%

16%

20%

Percent that rarely or never wear seat belts

Source: The World Almanac, 2003, 2009

From the graph, we see that in 2001 about 18% of male high school

students rarely or never wore seat belts. By 2007, the percent was about

14%, a decrease of 18% 14%, or 4%.

A pictograph is like a bar graph, but the bars

MEDICAL SCHOOLS Refer to the pictograph below. In 2008, how

are made from pictures or symbols. A key tells

many students were enrolled in California medical schools?

the meaning (or value) of each symbol.

Total Medical School Enrollment

by State, 2008

California

Missouri

Virginia

= 1,000 medical students

Chapter 7

Summary and Review

623

The California row contains 4 complete symbols and almost all of

another.This means that there were 4 1,000, or 4,000 medical students,

plus approximately 900 more. In 2008, about 4,900 students were

enrolled in California medical schools.

In a circle graph, regions called sectors (they

CHECKING

E-MAIL The

circle

4 or 5

look like slices of pizza) are used to show what

graph to the right shows the results of

part of the whole each quantity represents.

a survey of adults who were asked

One

6 or more

how many personal e-mail addresses

e-mail

address

they regularly check. What percent of

42%

the adults surveyed check 4 or more

2 or 3

e-mail

e-mail addresses regularly?

addresses

48%

Source: Ipsos for Habeas

We add the percent of the responses for 4 or 5 e-mail addresses and the

percent of the responses for 6 or more e-mail addresses:

5% + 5% = 10%

Thus, 10% of the adults surveyed check 4 or more e-mail addresses

regularly.

Use the survey results to predict the number of adults in a group of

5,000 that would check only one e-mail address regularly.

In the survey, 42% said they check only one e-mail address. We need to

ﬁnd:

What

number

42%

5,000?

42%

5,000

Translate.

x 0.42 5,000

Write 42% as a decimal.

x 2,100

Do the multiplication.

According to the survey, about 2,100 of the 5,000 adults would check

only one e-mail address regularly.

A line graph is used to show how quantities

SNOWBOARDING The line graph below shows the number of

change with time. From such a graph, we can

people who participated in snowboarding in the United States for the

determine when a quantity is increasing and

years 2000–2007.

when it is decreasing.

Number of people who participated

in snowboarding in the U.S.

	7.0
	6.0
	5.0
Millions	4.0
	3.0

	2.0
	1.0
	2000	2001	2002	2003	2004	2005	2006	2007
				Year

Source: National Ski & Snowboard Retailers Association

624		Chapter 7 Summary and Review

When did the popularity of snowboarding seem to peak?

The years with the highest participation were 2003 and 2004.

Between which two years was there the greatest decrease in the number of snowboarding participants?

The line segment with the greatest “fall” as we read left to right is the segment connecting the data points for the years 2005 and 2006. Thus, the greatest decrease in the number of snowboarding participants occurred between 2005 and 2006.

Two quantities that are changing with time can

SKATEBOARDING Refer to the line graphs below that show the

be compared by drawing both lines on the same

results of a skateboarding race.

graph.

Finish

traveled

Distance

Skateboarder 1

Start

Skateboarder 2

B C D

Observations:

•Since the red graph is well above the blue graph at time A, skateboarder 1 was well ahead of skateboarder 2 at that stage of the race.

•Since the red graph is horizontal from time A to time B, skateboarder 1 had stopped.

•Since the blue graph crosses the red graph at time B, at that instant, the skateboarders are tied for the lead.

•Since the blue graph crosses the dashed ﬁnish line at time C, which is sooner than time D, skateboarder 2 won the race.

A histogram is a bar graph with these features:

SLEEP A group of parents of

The bars of the histogram touch.

junior

high

students

were

120

surveyed and asked to estimate

100

Data values never fall at the edge of a

Frequency

the number of hours that their

bar.

children

slept

each night. The

The widths of the bars are equal and

results

are

displayed

the

represent a range of values.

histogram

the right. How

many children sleep 6 to 9 hours

a night?

3.5

5.5

7.5

9.5

11.5

Hours of sleep

The bar with edges 5.5 and 7.5 corresponds to the 6 to 7 hour range.The

height of that bar indicates that 42 children sleep 6 to 7 hours. The bar

with edges 7.5 and 9.5 corresponds to the 8 to 9 hour range. The height

of that bar indicates that 93 children sleep 8 to 9 hours. The total

number of children sleeping 6 to 9 hours is found using addition:

42 + 93 = 135

135 of the junior high children sleep 6 to 9 hours a night.

A frequency polygon is a special line graph formed from a histogram by joining the center points at the top of each bar. On the horizontal axis, we write the coordinate of the middle value of each class interval. Then we erase the bars.

Chapter 7 Summary and Review

625

Frequency polygon

		120
	Frequency	100
	Frequency	80
		80

4.5 6.5 8.5 10.5

Hours of sleep

REVIEW EXERCISES

Refer to the table below to answer the following questions.

1.WINDCHILL TEMPERATURES

a.Find the windchill temperature on a 10°F day when a 15-mph wind is blowing.

b.Find the windchill temperature on a –15°F day when a 30-mph wind is blowing.

2.WIND SPEEDS

a.The windchill temperature is 25°F, and the actual outdoor temperature is 15°F. How fast is the wind blowing?

b.The windchill temperature is 38°F, and the actual outdoor temperature is –5°F. How fast is the wind blowing?

Determining the Windchill Temperature

Wind			Actual temperature
Wind
speed	20°F	15°F	10°F	5°F	0°F	–5°F	–10°F	–15°F

5 mph	16°	12°	7°	0°	5°	10°	15°	21°
10 mph	3°	3°	9°	15°	22°	27°	34°	40°
15 mph	5°	11°	18°	25°	31°	38°	45°	51°
20 mph	10°	17°	24°	31°	39°	46°	53°	60°
25 mph	15°	22°	29°	36°	44°	51°	59°	66°
30 mph	18°	25°	33°	41°	49°	56°	64°	71°
35 mph	20°	27°	35°	43°	52°	58°	67°	74°

As of 2008,the United States had the most nuclear power plants in operation worldwide, with 104. The following bar graph shows the remainder of the top ten countries and the number of nuclear power plants they have in operation.

3.How many nuclear power plants does Korea have in operation?

4.How many nuclear power plants does France have in operation?

5.Which countries have the same number of nuclear power plants in operation? How many?

6.How many more nuclear power plants in operation does Japan have than Canada?

Number of Nuclear Power Plants in Operation

France
Japan
Russian Federation
Republic of Korea
United Kingdom
Canada
Germany
India
Ukraine
0	10	20	30	40	50	60

Source: International Atomic Energy Agency

626	Chapter 7 Summary and Review

In a workplace survey, employed adults were asked if they would date a co-worker. The results of the survey are shown below. Use the double-bar graph to answer the following questions.

7.What percent of the women said they would not date a co-worker?

8.Did more men or women say that they would date a co-worker? What percent more?

9.When asked, were more men or more women unsure if they would date a co-worker?

10.Which of the three responses to the survey was given by approximately the same percent of men and women?

Responses to the Survey:

Would you date a co-worker?

60%			Men
	43%		Men	43%
50%			Women
40%		31%
40%	28%		29%	26%
30%	28%		29%	26%
20%
10%
	Yes	No		Not sure

Source: Spherion Workplace Survey

Refer to the pictograph below to answer the following questions.

11.How many animals are there at the San Diego Zoo?

12.Which of the zoos listed has the most animals? How many?

13.How many animals would have to be added to the Phoenix Zoo for it to have the same number as the San Diego Zoo?

14.Find the total number of animals in all three zoos.

America’s Best Zoos

Number of Animals

San Diego Zoo

Columbus Zoo, Ohio

Phoenix Zoo

= 1,000 animals

Refer to the circle graph below to answer the following questions.

15.What element makes up the largest percent of the body weight of a human?

16.Elements other than oxygen, carbon, hydrogen, and nitrogen account for what percent of the weight of a human body?

17.Hydrogen accounts for how much of the body weight of a 135-pound woman?

18.Oxygen and carbon account for how much of the body weight of a 200-pound man?

Elements in the Human Body

(by weight)

3%
Nitrogen	Other elements
10%
Hydrogen
18%
Carbon	65%
	65%
	Oxygen

Source: General Chemistry Online

Refer to the line graph on the next page to answer the following questions.

19.How many eggs were produced in Nebraska in 2001?

20.How many eggs were produced in North Carolina in 2008?

21.In what year was the egg production of Nebraska equal to that of North Carolina? How many eggs?

22.What was the total egg production of Nebraska and North Carolina in 2005?

23.Between what two years did the egg production in North Carolina increase dramatically?

24.Between what two years did the egg production in Nebraska decrease dramatically?

25.How many more eggs did North Carolina produce in 2008 compared to Nebraska?

Source: USA Travel Guide

26.How many more eggs did Nebraska produce in 2000 compared to North Carolina?

Total Egg Production

	3,300	North Carolina
	3,300	Nebraska
		Nebraska
	3,200
	3,100
eggs	3,000
eggs
Million	2,900
Million	2,800
	2,800
	2,700
	2,600
	2,500
		2000 2001 2002 2003 2004 2005 2006 2007 2008
		Year

Source: U.S. Department of Agriculture

A survey of the weekly television viewing habits of 320 households produced the histogram in the next column.Use the graph to answer the following questions.

27.How many households watch between 1 and 5 hours of TV each week?

28.How many households watch between 6 and 15 hours of TV each week?

Chapter 7 Summary and Review

627

29.How many households watch 11 hours or more each week?

Survey of Hours of TV Watched Weekly

	110
	90
Frequency	70
	50
	30
	30
	10
	0.5	5.5	10.5	15.5	20.5	25.5

Hours of TV watched by the household

30.Create a frequency polygon from the histogram shown above.

		110
		90
	Frequency	70
	Frequency	50
		50
		30
		10

3.0 8.0 13.0 18.0 23.0

Hours of TV watched by the household

S E C T I O N 7.2 Mean, Median, and Mode

DEFINITIONS AND CONCEPTS		EXAMPLES
It is often beneﬁcial to use one number to		Find the mean of the following set of values:
represent the “center” of all the numbers in a		6	8	3	5	9	8	10	7	8	5
set of data. There are three measures of central		6	8	3	5	9	8	10	7	8	5
set of data. There are three measures of central
tendency: mean, median, mode.		To ﬁnd the mean, we divide the sum of the values by the number of
The mean of a set of values is given by the		values, which is 10.
The mean of a set of values is given by the
formula		6 8 3 5 9 8 10 7 8 5										69
Mean	sum of the values							10					10
Mean	number of values											6.9
		Thus, 6.9 is the mean.

628		Chapter 7 Summary and Review

When a value in a set appears more than once, that value has a greater “inﬂuence” on the mean than another value that only occurs a single time. To simplify the process of ﬁnding the mean, any value that appears more than once can be “weighted” by multiplying it by the number of times it occurs.

To ﬁnd the weighted mean of a set of values:

1.Multiply each value by the number of times it occurs.

2.Find the sum of the products from step 1.

3.Divide the sum from step 2 by the total number of individual values.

A student’s grade point average (GPA) can be found using a weighted mean.

Some schools assign a certain number of credit hours to a course while others assign a certain number of units.

To ﬁnd the median of a set of values:

1.Arrange the values in increasing order.

2.If there is an odd number of values, the median is the middle value.

3.If there is an even number of values, the median is the mean (average) of the middle two values.

The mode of a set of values is the single value that occurs most often.

GPAs Find the semester grade point average for a student that received the following grades. (The point values are A = 4, B = 3, C = 2, D = 1, and F = 0.)

Course	Grade	Credits

Algebra	A	5
History	C	3
Art	D	4

Multiply the number of credits for each course by the point value of the grade received. Add the results (as shown in blue) to get the total number of grade points. To ﬁnd the total number of credits, add as shown in red.

Course	Grade	Credits		Weighted grade points

Algebra	A		5	4	5	→	20
History	C		3	2	3	→	6
Art	D		4	1	4	→	4
Totals			12				30

To ﬁnd the GPA, we divide.

GPA			30		The total number of grade points
					The total number of credits
			12
			12
		2.5 Do the division.
The student’s semester GPA is 2.5.
To ﬁnd the median of
6	8	3	5	9		8	10	7	8	5
arrange them in increasing order:
Smallest										Largest
	3	5	5	6				8	8	9 10 There are 10 values.
	3	5	5	6		7	8	8	8	9 10 There are 10 values.

Middle two values

Since there are an even number of values, the median is the mean (average) of the two middle values:

7 8			15	7.5
	2		2	7.5
Thus, 7.5 is the median.
To ﬁnd the mode of
6	8	3	5	9	8	10	7	8	5

we ﬁnd the value that occurs most often.

6	8	3	5	9	8	10	7	8	5

3 times

Since 8 occurs the most times, it is the mode.

									Chapter 7 Summary and Review		629


When a collection of values has two modes, it is	The collection of values
called bimodal.	1	2	3	3	4	5	6	6	7	8
	1	2	3	3	4	5	6	6	7	8
	has two modes: 3 and 6.

REVIEW EXERCISES

31.GRADES Jose worked hard this semester, earning grades of 87, 92, 97, 100, 100, 98, 90, and 98. If he needs a 95 average to earn an A in the class, did he make it?

32.GRADE SUMMARIES The students in a mathematics class had ﬁnal averages of 43, 83, 40, 100, 40, 36, 75, 39, and 100. When asked how well her students did, their teacher answered, “43 was typical.” What measure was the teacher using: mean, median, or mode?

33.PRETZEL PACKAGING Samples of SnacPak pretzels were weighed to ﬁnd out whether the package claim “Net weight 1.2 ounces” was accurate. The tally appears in the table. Find the mode of the weights.

Weights of

SnacPak Pretzels

Ounces Number

0.91

1.06

1.118

1.223

1.32

1.40

34.Find the mean weight of the samples in Exercise 33.

35.BLOOD SAMPLES A medical laboratory technician examined a blood sample under a microscope and measured the sizes (in microns) of the white blood cells. The data are listed below. Find the mean, median, and mode.

7.8

6.9

7.9

6.7

6.8

8.0

7.2

6.9

7.5

36.	SUMMER READING A paperback version of the
	classic Gone With the Wind is 960 pages long. If a
	student wants to read the entire book during the
	month of June, how many pages must she average
	per day?
37.	WALK-A-THONS Use the data in the table
	to ﬁnd the mean (average) donation to a charity
	walk-a-thon.

	Donation amount		$5		$10	$20		$50	$100

	Number received		20		65	25		5	10

38.	GPAs Find the semester grade point average for a
	student that received the grades shown below.
	Round to the nearest hundredth. (Assume the
	following standard point values for the letter grades:
	A = 4, B = 3, C = 2, D = 1, and F = 0.)

		Course	Grade			Credits

		Chemistry		A			5
		Sociology		C			3
		Economics		D			4
		Archery		A			1

630
C H A P T E R 7				TEST
Fill in the blanks.
1. a.	A horizontal or vertical line used for reference in
	a bar graph is called an				.
b.	The		(average) of a set of values is the sum
	of the values divided by the number of values in
	the set.
c.	The			of a set of values written in
	increasing order is the middle value.
d.	The		of a set of values is the single value
	that occurs most often.
e.	The mean, median, and mode are three measures
	of	tendency.

2.WORKOUTS Refer to the table below to answer the following questions.

Number of Calories Burned While Running for One Hour

Running		Body Weight
Running
speed (mph)	130 lb	155 lb	190 lb

5	472	563	690
6	590	704	863
7	679	809	992
8	797	950	1,165
9	885	1,056	1,294

Source: nutristrategy.com

a.How many calories will a 155-pound person burn if she runs for one hour at a rate of

5 mph?

b.In one hour, how many more calories will a 190-pound person burn if he runs at a rate of 7 mph instead of 6 mph?

c.At what rate does a 130-pound person have to run for one hour to burn approximately 800 calories?

3.MOVING Refer to the bar graph in the next column to answer the following questions.

a.Which piece of furniture shown in the graph requires the greatest number of feet of bubble wrap? How much?

b.How many more feet of bubble wrap is needed to wrap a desk than a coffee table?

c.How many feet of bubble wrap is needed to cover a bedroom set that has a headboard, a dresser, and two end tables?

Amount of Bubble Wrap Needed to Wrap

Pieces of Furniture When Moving

Bed headboard
Coffee table
Desk
Dresser
End table
Chair (living room)
Love seat
Rocker
20	40	60	80	100	120	140	160
		Feet of bubble wrap

Source: transitsystems.com

4.CANCER SURVIVAL RATES Refer to the graph below to answer the following questions.

a.What was the survival rate (in percent) from breast cancer in 1976?

b.By how many percent did the cancer survival rate for breast cancer increase by 2006?

c.Which type of cancer shown in the graph has the lowest survival rate?

d.Which type of cancer has had the greatest increase in survival rate from 1976 to 2006? How much of an increase?

Five-Year Survival Rates

		99.7%		1976
100%	89.1%			2006
100%
90%
90%	75%
80%		67%	65.2%
70%		67%	65.2%
60%			50%
50%			50%
50%
40%
30%					15.6%
20%				13%
10%				13%
10%
	Breast	Prostate	Colon	Lung

Source: SEER Cancer Statistics Review

5.ENERGY DRINKS Refer to the pictograph below to answer the following questions.

Sugar Content in Energy Drinks and Coffee

(12-ounce serving)

Monster Energy Drink

Big Red Energy Drink

Starbucks Tall Caffè Mocha

= 10 grams sugar

Source: energyfiend.com

a.How many grams of sugar are there in 12 ounces of Big Red?

b.For a 12-ounce serving, how many more grams of sugar are there in Monster Energy Drink than in Starbucks Tall Caff´e Mocha?

6.FIRES Refer to the graph below to answer the following questions.

a.In 2007, what percent of the ﬁres in the United States were vehicle ﬁres?

b.In 2007, there were a total of 1,557,500 ﬁres

in the United States. How many were structure ﬁres?

Where Fires Occurred, 2007

Vehicle

fires

Outside fires

Structure 49% fires

34%

Source: U.S. Fire Administration

7.NYPD Refer to the graph in the next column to answer the following questions.

a.How many uniformed police ofﬁcers did the NYPD have in 1987?

b.When was the number of uniformed police ofﬁcers the least? How many ofﬁcers were there at that time?

c.When was the number of uniformed police ofﬁcers the greatest? How many ofﬁcers were there at that time?

Chapter 7 Test

631

d.Find the decrease in the number of uniformed police ofﬁcers from 2000 to 2003.

New York City Police Department

Number of Uniformed Police Officers

		45
		40
	Thousands	35
	Thousands	30
		30
		25
		20

’87 ’90 ’95 ’00 ’05 ’08 Year

Source: New York Times, July 17, 2009

8.BICYCLE RACES Refer to the graph below to answer each of following questions about a two-man bicycle race.

a.Which bicyclist had traveled farther at time A?

b.Explain what was happening in the race at time B.

c.When was the ﬁrst time that bicyclist 2 stopped to rest?

d.Did bicyclist 2 ever lead the race? If so, at what time?

e.Which bicyclist won the race?

Ten-Mile Bicycle Race

Finish
traveled
Distance			Bicyclist 1
Distance			Bicyclist 2
Start
A	B C	D	Time

632	Chapter 7 Test

9.COMMUTING TIME A school district collected data on the number of minutes it took its employees to drive to work in the morning. The results are presented in the histogram below.

a.How many employees have a commute time that is in the 7-to-10-minute range?

b.How many employees have a commute time that is less than 10 minutes?

c.How many employees have a commute that takes 15 minutes or more each day?

School District Employees’ Commute

	40			35
				35
Frequency	30				28
			22			20
	20					20
	20
	10	8					9
							9


	2.5	6.5	10.5	14.5	18.5	22.5	26.5

Morning commute time (min)

10.VOLUNTEER SERVICE The number of hours served last month by each of the volunteers at a homeless shelter are listed below:

4 6 8 2 8 10 11 9 5 12 5 18 7 5 1 9

a.Find the mean (average) of the hours of volunteer service.

b.Find the median of the hours of volunteer service.

c.Find the mode of the hours of volunteer service.

11.RATING MOVIES Netﬂicks, a popular online DVD rental system, allows members to rate movies using a 5-star system. The table below shows a tally of the ratings that a group of college students gave a movie. Find the mean (average) rating of the movie.

Number of Stars	Comments	Tally
	Loved it	III
	Really liked it	IIII
	Liked it	IIII
	Didn’t like it	IIII I
	Hated it	II

12.GPAs Find the semester grade point average for a student who received the following grades. Round to the nearest hundredth.

Course	Grade	Credits

WEIGHT TRAINING	C	1
TRIGONOMETRY	A	3
GOVERNMENT	B	2
PHYSICS	A	4
PHYSICS LAB	D	1

13.RATINGS The seven top-rated cable television programs for the week of March 30–April 5, 2009, are given below. What are the mean, median, and mode of the viewer data?

Show/day/time/network	Millions of viewers

WCW Raw, Mon. 10 P.M., USA	5.39
WCW Raw, Mon. 9 P.M., USA	4.99
NCIS, Tue. 7 P.M., USA	4.25
NCIS, Wed. 7 P.M., USA	4.25
NCIS, Mon. 7 P.M., USA	4.04
Penguins of Madagascar,	4.02
Sun. 10 A.M., Nickelodeon
The O’Reilly Factor,	3.93
Wed. 8 P.M., Fox

Source: Bay Ledger News Zone

14.REAL ESTATE In May of 2009, the median sales price of an existing single-family home in the United States was $172,900. Explain what is meant by the median sales price. (Source: National Association of Realtors)

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25.	8	10		16		63		6			7
26.	7	2		11		5		4		17
27.	39	1		50		41		51			47
28.	47	18		35			29			27	16
29.	1.8	1.7				2.0		9.0			2.1	2.3	2.1	2.0
30.	5.0	1.3				5.0		2.3			4.3	5.6	3.2	4.5
31.	1		11		13		2		3		7
31.	5	5		5			5	5			5
32.	1	2		7		11		13			29

	9	9		9		9		9			9

25.	8	10		16		63		6			7
26.	7	2		11		5		4		17
27.	39	1		50		41		51			47
28.	47	18		35			29			27	16
29.	1.8	1.7				2.0		9.0			2.1	2.3	2.1	2.0
30.	5.0	1.3				5.0		2.3			4.3	5.6	3.2	4.5
31.	1		11		13		2		3		7
31.	5	5		5			5	5			5
32.	1	2		7		11		13			29

	9	9		9		9		9			9

25.	8	10		16		63		6			7
26.	7	2		11		5		4		17
27.	39	1		50		41		51			47
28.	47	18		35			29			27	16
29.	1.8	1.7				2.0		9.0			2.1	2.3	2.1	2.0
30.	5.0	1.3				5.0		2.3			4.3	5.6	3.2	4.5
31.	1		11		13		2		3		7
31.	5	5		5			5	5			5
32.	1	2		7		11		13			29

	9	9		9		9		9			9