6.1 Reading Circle, Bar and Line Graphs

A graph shows information visually. The type of graph usually depends on the kind of information

being disclosed.

To read a graph:

• Examine the title of the graph to find out what information is shown.

• Examine the parts to see how they relate to one another and to the whole.

• Examine the labels for each part of the graph and any explanatory remarks that may be given.

• Use the parts to calculate additional amounts or percents.

A circle or pie graph uses a circle to show pictorially how a whole is

divided into parts. The complete circle represents one whole

quantity. The circle is divided into parts so that the sum of the parts

equals the whole. These parts can be fractions, decimals, or percents.

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Favorite Breakfasts

cereal42%

pancakes11%waffles

7%

toast6%

doughnuts8%

eggs20%

other6%

Example A•The following circle graph shows the favorite breakfast foods for students.

•a. What is the most

popular item?

•b. What percent of the

students favorite breakfast

food is eggs and

pancakes?

cereal

20 + 11 = 31%

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Favorite Breakfasts

cereal42%

pancakes11%waffles

7%

toast6%

doughnuts8%

eggs20%

other6%

Example A•The following circle graph shows the favorite breakfast foods for 300 students.

•a. How many students

prefer pancakes?

11% of 300 = 33

• What % of the gross pay is used for insurance?

• 11%

Distribution of wholesale price for a $425 color television.

Taxes$40

Materials $125

Labor $130

Overhead $80

Profit $50

• What percent of the wholesale price is the cost of labor?

• What would the wholesale price be if no tariff (taxes) was paid on imported parts?

%6.30425100130425

130

100

%?

385$40$425$

A bar graph uses two or more bars to compare two or more amounts.

The bar lengths represent the amounts being compared. Bars can

be drawn either vertical or horizontal. Labels describe the bars

and the amount of each bar.

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 Recipe Chicken Sandwich

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

How much fat is in a subway meatball sandwich?

about 16 grams

Which item contains the most fat?

Burger King’s Whopper

Which item contains about 23 g of fat?KFC’s Original Recipe

Chicken Sandwich

Company Oil Production

0 1 2 3 4 5 6 7

1980

1985

1990

1995

2000

2005

Yea

r

100 milion barrels

How many more 100 million barrels of oil are indicated for the company in 2005 than in 1985? 75.1475.5

Judging from the graph, should company oil production in 2010 be more or less than in 2005?

Line graphs use one or more lines to show changes in data. Normally

the horizontal axis represents periods of time or specific times and the vertical axis gives the

numerical amounts.

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Lake Mead Average Water Level

1100

11201140

1160

1180

12001220

1240

1940 1950 1960 1970 1980 1990 2000 2005

Year

Hei

gh

t in

fee

t

For which year was the water level the lowest?

2005For which year was the water level the highest?2000

Between what two years was the increase in water level the greatest?

1970 and 1980

http://hwww.arachnoid.com/NaturalResources/index.html

Petroleum products supplied by type in the U.S.

Mill

ion

barr

els

per d

ay

What year was the motor gasoline supply 6,580,000 barrels of oil?

For which 10-year period was the increase in jet fuel the greatest?

1980

1960 to 1970

In 2000 the supply of jet fuel was what percent of the motor gasoline supply? 20.3%By what percent did jet fuel supplied increase from 1960 to 2000? 507.1 %

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•Circle graphs, bar graphs, and line graphs provide three ways of representing a collection of data visually.

•Sometimes it is useful to describe a set of data numerically, using statistics.

•A statistic is simply a number that describes a set of data.

An average is an approximate number that is a central value of a

set of data. The most common average is the arithmetic mean or

statistical mean.

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Average

To find the average or mean of a set of numbers, add the numbers and then divide by the number of data items. This is shown symbolically as:

where the Greek letter sigma is a summation symbol and indicates the addition of a set of values.

n

xx i

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Example A

•Roberto bowled a 175, 210 and 162. Find •his bowling average.•Solution•To find the mean we add the scores together and then divide by the number of scores, 3:

•Roberto’s bowling average is 182.

175 210 162

3

547

3 182.33

Besides the mean, we also use the median and the mode to describe groups of data. These are all called

measures of central tendency. They are used to determine the center of a set of data using a

different perspective.

The median is the middle value when the data values are arranged

in order of size. If there is an even number of data then the median is the average of

the 2 middle values.

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•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 two middle numbers are 72,000 and 81,000

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• Median

• The median salary is $76,500.

$72,000 $81,000

2

$153,000

2

$76,500

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ModeThe 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.

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Example F

•Find the mode of these data.•23, 24, 27, 27, 18, 29•Solution•The number that occurs most often is 27.

•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.

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• 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• Solution• 1. 8, 12, 15, 27, 31, 42 There is no mode.• The modes are 55 and 67.• 44, 55, 55, 55, 62, 65, 67, 67, 67, 72,

73, 75