Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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46 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA FIGURE 2.6 Minitab Output of Credit Card Balance Histogram Minitab Instructions: 1. Open file: Capital.MTW. 2. Choose Graph > Histogram. 3. Click Simple. 4. Click OK. 5. In Graph variables, enter data column. 6. Click OK. Issues with Excel If you use Excel to construct a histogram as indicated in the instructions in Figure 2.5, the initial graph will come up with gaps between the bars. Because histograms illustrate the distribution of data across the range of all possible values for the quantitative variable, histograms do not have gaps. Therefore, to get the proper histogram format, you need to close these gaps by setting the gap width to zero, as indicated in the Excel instructions shown in Figure 2.5. Minitab provides no gaps with its default output, as shown in Figure 2.6. SUMMARY Constructing Frequency Histograms To construct a frequency histogram, perform the following steps: 1. Follow the steps for constructing a frequency distribution (see Examples 2-1 or 2-3). 2. Use the horizontal axis to represent the variable of interest. Use the vertical axis to represent the frequency in each class. 3. Draw vertical bars for each class or data value so that the heights of the bars correspond to the frequencies. Make sure there are no gaps between the bars. (Note, if the classes do not have equal widths, the bar height should be adjusted to make the area of the bar proportional to the frequency.) 4. Label the histogram appropriately. EXAMPLE 2-4 Frequency Histograms TRY PROBLEM 2.10 Emergency Response Times The director of emergency responses in Montreal, Canada, is interested in analyzing the time needed for response teams to reach their destinations in emergency situations after leaving their stations. She has acquired the response times for 1,220 calls last month. To develop the frequency histogram, perform the following steps:
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 47 Step 1 Construct a frequency distribution. Because response time is a continuous variable measured in seconds, the data should be broken down into classes and the steps given in Example 2-3 should be used. The following frequency distribution with 10 classes was developed: Response Time Frequency Response Time Frequency 0 and under 30 36 180 and under 210 145 30 and under 60 68 210 and under 240 80 60 and under 90 195 240 and under 270 43 90 and under 120 180 270 and under 300 31 120 and under 150 260 Total 1,220 150 and under 180 182 Step 2 Construct the axes for the histogram. The horizontal axis will be response time and the vertical axis will be frequency. Step 3 Construct bars with heights corresponding to the frequency of each class and label appropriately. This is shown as follows: 300 Emergency Response Time Distribution 250 200 Frequency 150 100 50 0 0 30 60 90 120 150 180 210 240 270 300 Emergency Response Times (Seconds) This histogram indicates that the response times vary considerably. The center is somewhere in the range of 120 to 180 seconds. Relative Frequency Histograms and Ogives Histograms can also be used to display relative frequency distributions and cumulative relative frequency distributions. A relative frequency histogram is formed in the same manner as a frequency histogram, but relative frequencies are used rather than frequencies. The cumulative relative frequency is presented using a graph called an ogive. Example 2-5 illustrates each of these graphical tools.
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Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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