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.

Slide 5- 5 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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 = 31%

Slide 5- 6 Copyright © 2008 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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. 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?

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 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

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

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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

Petroleum products supplied by type in the U.S. Million barrels per day 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? 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 %

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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.

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.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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 The two middle numbers are 72,000 and 81,000

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley Median The median salary is $76,500.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley Mode The 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.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley 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.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison- Wesley Find the mode or modes of these data: 1. 8, 12, 15, 27, 31, , 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 , 55, 55, 55, 62, 65, 67, 67, 67, 72, 73, 75