1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 6.2 Reading Graphs

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Objectives o Learn the purposes and properties of graphs. o Read bar graphs. o Read circle graphs. o Read line graphs. o Read histograms.

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The Purpose of Four Types of Graphs 1.Bar Graphs: to emphasize comparative amounts. 2.Circle Graphs: to help in understanding percents or parts of a whole. Circle graphs are also called pie charts. 3.Line Graphs: to indicate tendencies or trends over a period of time. 4.Histograms: to indicate data in classes (a range or interval of numbers).

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Reading a Bar Graph Examine the following bar graph. Note that the scale on the left (sales) and the categories at the bottom (months) are clearly labeled and the graph itself has a title.

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Reading a Bar Graph (cont.) Solution The following questions can be answered by reading information directly from the graph. a.What were the sales in January? (Note that the scale on the left of the graph says that sales are in thousands of dollars.) $100,000 b.During what month were sales lowest? March

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 1: Reading a Bar Graph (cont.) c.During what month were sales highest? February and June d. What were the sales during each of the highest sales months? $150,000 e.What were the sales in April? $75,000

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. The following questions can be answered by reading information from the graph and making some calculations. f. What was the amount of decrease in sales between February and March? Example 1: Reading a Bar Graph (cont.)

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. g.What was the percent of decrease in sales from February to March? Example 1: Reading a Bar Graph (cont.)

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2: Reading a Circle Graph Examine the following circle graph. Percents budgeted for various items in a household for one year are given. Use the information in the graph to calculate what amount will be allocated to each item indicated if the family income was $45,000.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Solution Example 2: Reading a Circle Graph (cont.)

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Reading a Line Graph Examine the following line graph. This graph shows the relationships between daily high and low temperatures. You can tell that temperatures tended to rise during the week but fell sharply on Saturday. (Note that the temperature scale on the left does not start at 0. There is a break indicated in that scale). Find the mean of the differences between the daily high and low temperatures for the week shown.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 3: Reading a Line Graph (cont.) Solution First, find the differences for each day. Then, find the mean of these differences.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Sunday:66 – 60=6  Monday:70 – 62=8  Tuesday:76 – 66=10  Wednesday:72 – 66=6  Thursday:80 – 68=12  Friday:80 – 70=10  Saturday:74 – 62=12  64  total of differences Example 3: Reading a Line Graph (cont.)

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Terms Related to Histograms Class: an interval (or range) of numbers that contains data items. Lower class limit: the smallest whole number that belongs to a class. Upper class limit: the largest whole number that belongs to a class.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Terms Related to Histograms (cont.) Class boundaries: numbers that are halfway between the upper limit of one class and the lower limit of the next class. Class width: the difference between the class boundaries of a class (the width of each bar). Frequency: the number of data items in a class.

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Reading a Histogram Examine the following histogram. This histogram summarizes the scores of 50 students on an English placement test. Refer to the graph to answer the following questions. Solution a.How many classes are represented? 6

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Reading a Histogram (cont.) b.What are the class limits of the first class? 201 and 250 c.What are the class boundaries of the second class? 250.5 and 300.5 d.What is the width of each class? 50 e.Which class has the greatest frequency? second class

18. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 4: Reading a Histogram (cont.) f.What is this frequency? 16 g.What percent of the scores are between 200.5 and 250.5? h.What percent of the scores are above 400.5?

19. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems 1.Using the bar graph in Example 1, what was the amount of increase in sales between March and April? 2.Using the circle graph in Example 2, if the person’s income decreases to $30,000 and the percent spent on each item does not change, what is the amount spent on entertainment over the year?

20. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problems (cont.) 3.Using the line graph in Example 3, find the minimum difference between the high and low temperatures of a single day in the week shown. 4.Using the histogram in Example 4, what is the frequency of the class with the least frequency?

21. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Practice Problem Answers 1.$25,000 2. $1500 3.6° 4. 2