1. Graphs Chapter 15 Sections 15.1-15.4

2. Copyright © Cengage Learning. All rights reserved. Bar Graphs 15.1

3. Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, and presentation of masses of numerical data. We will first study the different ways in which data can be presented using graphs. Then, we will study some of the different ways to describe small sets of data. We will study only the most basic parts to help you read and better understand newspapers, magazines, and some of the technical reports in your field of interest. Bar Graphs

4. A graph is a picture that shows the relationship between several types of collected information. A graph is very useful when there are large quantities of information to analyze. There are many ways of graphing. A bar graph is a graph with parallel bars whose lengths are proportional to the frequency of the given quantities in a data set. Bar Graphs

6. What are the monthly earnings of a data-processing technician with two years of experience? Find the data-processing technician in the “Classification of workers” column. Read the right end of the bar on the “Monthly salary” scale: Since the end of the bar falls between $3000 and $3500 we need to estimate the amount. Since it is just under half way up we can say it is $3300-3400. Example 1

7. Copyright © Cengage Learning. All rights reserved. Circle Graphs 15.2

8. Another type of graph used quite often to give results of surveys is the circle graph Circle Graphs U.S. Labor Force in 1930 U.S. Labor Force in 2000

9. A circle graph is a circle whose radii divide the circle into sectors that are proportional in angle and area in relative size to the quantities represented. The circle graph is used to show the relationship between the parts and the whole. Since there are 360 degrees in a circle, multiply the percent of an item by 360 to find what part of the circle is used by that item. Circle Graphs

10. Draw a circle graph with the following data. In 1930, 58% of the people working had a grade school education or less, 32% had a high school education, and 10% had a college education. To make a circle graph with data given in percents, first draw the circle. Then convert the %s given to sizes of the circle by using 360 degrees for the whole amount and figuring out the part that relates to the % given. 58% of 360  = 0.58  360  = 208.8 , or about 209  32% of 360  = 0.32  360  = 115.2 , or about 115  10% of 360  = 0.10  360  = 36  Example 1

11. With a protractor draw central angles of 209 , 115 , and 36 . Then label the sections. Example 1 Education of Labor Force in 1930

12. Sometimes data are not written in percent form. When a circle graph is to be drawn from data that are not in percent form, the data must be converted to percents. Once the data are in this form, the steps in drawing the graph are the same as those already given. Circle Graphs

13. Example Make a circle graph to illustrate this data: Hours spent in class for 2yr. Engineering degree: Math10, Science 10, Technical classes 34, General Ed. 12 Total= 66 First convert each piece of data to a % of the total of the total hours: Ex. Math 10?_so 10(100) = 15.2% 66 100 66 Using this same process then science= 15.2%, Tech. = 51.5%, Gen. Ed. = 18.2% Next convert each % to a part of the circle out of 360 degrees so Math = 55, Science = 55, Tech. = 185, and Gen. Ed. = 66 Then draw a circle illustrating those divisions.

14. Copyright © Cengage Learning. All rights reserved. Line Graphs 15.3

15. A line graph is a graph formed by segments of straight lines that join the plotted points that represent given data. The line graph is used to show changing conditions, often over a certain time interval. Line Graphs

16. An industrial technician must keep a chemical at a temperature below 60  F. He must also keep an hourly record of its temperature and record each day’s temperatures on a line graph. The following table shows the data he collected. Example 1

17. When drawing line graphs, 1. draw horizontal and vertical scales 2. name and label each scale so that all marks on the scale are the same distance apart and show equal intervals 3. plot the points from the given data; 4.connect each pair of points in order by a straight line. Example 1

18. When you have taken all these steps, you will have a line graph similar to this one Example 1 cont ’ d

19. Copyright © Cengage Learning. All rights reserved. Other Graphs 15.4

20. A graph can be a curved line.This graph shows typical power gain for class B push-pull amplifiers with 9-volt power supply. Other Graphs

21. What is the power output in this graph when the gain is 22 decibels (dB)? Find 22 on the horizontal axis and read up until you meet the graph. Read left to the vertical axis and read 160 milliwatts (mW). Example 1

22. Practice Problems Ch. 15 Pg. 521 1-20; Pg. 525 1-9 odds & 14-15; Pg. 527-528 1 & 9-14