section 2.2

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Section 2.2

Graphical Displays of Data2.2b(ii) - Histogram






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

Class Frequency Midpoint Class Boundaries$1500 - $1599

$1600 - $1699

$1700 - $1799

$1800 - $1899

$1900 - $1999

2

5

4

5

4

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






Example 2.12: Constructing a Histogram (cont.)

Solution






Example 2.12: Constructing a Histogram (cont.)






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

Class Frequency Relative Frequency

$1500 - $1599

$1600 - $1699

$1700 - $1799

2

5

4

2 10.1 10%

20 10

5 10.25 25%

20 4

4 10.2 20%

20 5






Example 2.13: Constructing a Relative Frequency Histogram (cont.)

3-D TV Prices (cont.)

Class Frequency Relative Frequency

$1800 - $1899

$1900 - $1999

5

4 4 10.2 20%

20 5

5 10.25 25%

20 4






Example 2.13: Constructing a Relative Frequency Histogram (cont.)

Solution






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






Example T.4: Using Microsoft Excel to Create a Histogram (cont.)

SolutionBegin 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.







Click on Labels if the first cells in yourinput 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.







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.







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.







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.







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.







• Format the Data Series to add the solid line border around the bars.







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






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

TI-84 Histogram

2ND 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.

section 2.2

Documents

success counts

histogram cont

relative frequency histogram

d tv prices cont

data labels

frequency distribution

data tab

data analysis