1. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Section 2.2 Graphical Displays of Data 2.2b(ii) - Histogram

2. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.12: Constructing a Histogram Construct a histogram of the 3-D TV prices from the previous section. The frequency distribution of the data is restated here. 3-D TV Prices ClassFrequencyMidpointClass Boundaries $1500 - $1599 $1600 - $1699 $1700 - $1799 $1800 - $1899 $1900 - $1999 2545425454 1549.5 1649.5 1749.5 1849.5 1949.5 1499.5 – 1599.5 1599.5 – 1699.5 1699.5 – 1799.5 1799.5 – 1899.5 1899.5 – 1999.5

3. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.12: Constructing a Histogram (cont.) Solution

4. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.12: Constructing a Histogram (cont.)

5. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.13: Constructing a Relative Frequency Histogram Construct a relative frequency histogram of the 3-D TV prices from the previous section. The frequency distribution of the data is reprinted here. 3-D TV Prices ClassFrequencyRelative Frequency $1500 - $1599 $1600 - $1699 $1700 - $1799 254254

6. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.13: Constructing a Relative Frequency Histogram (cont.) 3-D TV Prices (cont.) ClassFrequencyRelative Frequency $1800 - $1899 $1900 - $1999 5454

7. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example 2.13: Constructing a Relative Frequency Histogram (cont.) Solution

8. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram Let’s recreate the histogram of 3-D TV prices using Microsoft Excel. The data are reprinted below. 3-D TV Prices (in Dollars) 1595 1699 1799 1899 1599 1699 1885 1984 1685 1757 1888 1999 1699 1787 1899 1999 1699 1799 1899 1999

9. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) Solution Begin by entering the data in column A in Excel. Next, enter the upper boundaries of the classes you want to use in Column B. Otherwise, the class boundaries will be chosen for you and may not be the best choice. Once your data are entered, go to the Data tab, then Data Analysis. Choose Histogram from the menu and click OK. The Input Range is where your data are located. The Bin Range is where your upper class boundaries have been entered.

10. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) Click on Labels if the first cells in your input range and bin range are data labels. Next, click on Chart Output to create a histogram instead of just a frequency distribution. Finally, click OK to generate the output.

11. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) When your histogram has been created, you will notice that the bars do not touch. To correct this error, click on one of the bars in the histogram.

12. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) Click on the Layout tab under Chart Tools. Click on the Format Selection button on the far left. The first option is Series Options. Move the Gap Width slider to No Gap and click on Close. You will also notice that the class boundaries are appearing on the x-axis where the midpoints should be, and there is a “More” category on the graph. To correct these errors, go to the Excel worksheet where the histogram’s frequency distribution is located. Change the bins to be the midpoints and delete the “More” entry from the spreadsheet.

13. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) Once these adjustments are made, the graph will be a histogram like the one shown in the following screenshot. Notice that this histogram does not look like the one you saw earlier in the chapter.

14. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) In order to change the histogram you just created to look like the one shown at the end of this example, several additional steps have to be taken to tweak the options of the chart. You must: Delete the whole row of the spreadsheet that contained the “More” category. Change the size, title, and axis labels. Turn off the legend. Format the Plot Area to have a gray background and darker gray border.

15. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) Format the Data Series to add the solid line border around the bars.

16. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.4: Using Microsoft Excel to Create a Histogram (cont.) By using the Microsoft online help for Excel or taking a class on Excel, you can explore all of the various options that can be used to customize your charts and graphs to change their appearance in countless ways

17. HAWKES LEARNING SYSTEMS Students Matter. Success Counts. Copyright © 2013 by Hawkes Learning Systems/Quant Systems, Inc. All rights reserved. Example T.1: Using a TI-83/84 Plus Calculator to Create a Histogram Use a TI ‑ 83/84 Plus calculator to recreate the histogram of our 3-D TV prices. The prices are reprinted below for your convenience. Put data into a TI-84 List. 3-D TV Prices (in Dollars) 1595 1699 1799 1899 1599 1699 1885 1984 1685 1757 1888 1999 1699 1787 1899 1999 1699 1799 1899 1999

18. TI-84 Histogram 2 ND Y= for STAT PLOT; ZOOM 9:ZoomStat to draw it. What are the good and bad of a TI-84 histogram? TRACE can help you informally explore what it drew.