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

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48 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA EXAMPLE 2-5 Relative Frequency Histograms and Ogives TRY PROBLEM 2.16 Emergency Response Times (continued) Example 2-4 introduced the situation facing the emergency response manager in Montreal. In that example, she formed a frequency distribution for a sample of 1,220 response times. She is now interested in graphing the relative frequencies and the cumulative relative frequencies. To do so, use the following steps: Step 1 Convert the frequency distribution into relative frequencies and cumulative relative frequencies. Cumulative Relative Response Time Frequency Relative Frequency Frequency 0 and under 30 36 36/1220 0.0295 0.0295 30 and under 60 68 68/1220 0.0557 0.0852 60 and under 90 195 195/1220 0.1598 0.2451 90 and under 120 180 180/1220 0.1475 0.3926 120 and under 150 260 260/1220 0.2131 0.6057 150 and under 180 182 182/1220 0.1492 0.7549 180 and under 210 145 145/1220 0.1189 0.8738 210 and under 240 80 80/1220 0.0656 0.9393 240 and under 270 43 43/1220 0.0352 0.9746 270 and under 300 31 31/1220 0.0254 1.0000 1,220 1.0000 Step 2 Construct the relative frequency histogram. Place the quantitative variable on the horizontal axis and the relative frequencies on the vertical axis. The vertical bars are drawn to heights corresponding to the relative frequencies of the classes. .25000 Emergency Response Time Relative Frequency Distribution .20000 Relative Frequency .15000 .10000 .05000 .00000 0 30 60 90 120 150 180 210 240 270 300 Response Times (seconds) Note the relative frequency histogram has exactly the same shape as the frequency histogram. However, the vertical axis has a different scale. Step 3 Construct the ogive. Draw a line connecting the points plotted above the upper limit of each class at a height corresponding to the cumulative relative frequency.
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 49 Cumulative Relative Frequency 1.00000 .90000 .80000 .70000 .60000 .50000 .40000 .30000 .20000 .10000 .00000 Emergency Response Times Ogive 0 30 60 90 120 150 180 210 240 270 300 Response Times CHAPTER OUTCOME #3 Joint Frequency Distributions Frequency distributions are effective tools for describing data. Thus far we have discussed how to develop grouped and ungrouped frequency distributions for one variable at a time. For instance, in the Capital Credit Union example, we were interested in customer credit card balances for all customers. We constructed a frequency distribution and histogram for that variable. However, often we need to examine the data more closely. This may involve constructing a joint frequency distribution for two variables. Joint frequency distributions can be constructed for qualitative or quantitative variables. SUMMARY Constructing Joint Frequency Distributions A joint frequency distribution is constructed using the following steps: 1. Obtain a set of data consisting of paired responses for two variables. The responses can be qualitative or quantitative. If the responses are quantitative, they can be discrete or continuous. 2. Construct a table with r rows and c columns, in which the number of rows represents the number of categories (or numeric classes) of one variable and the number of columns corresponds to the number of categories (or numeric classes) of the second variable. 3. Count the number of joint occurrences at each row level and each column level for all combinations of row and column values and place these frequencies in the appropriate cells. 4. Compute the row and column totals, which are called the marginal frequencies. 5. If a joint relative frequency distribution is desired, divide each cell frequency by the total number of paired observations. EXAMPLE 2-6 Joint Frequency Distribution Pizza Hut Pizza Hut is a national pizza chain that has franchises in every major city in the United States and many foreign countries. Recently, the manager at a Minnesota store collected data dealing with customer purchases. Among the data collected were
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Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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