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# Fixed Intervals Help (page 2)

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By — McGraw-Hill Professional
Updated on Aug 26, 2011

## Variable-Width Histogram

Histograms were introduced back in Chapter 1. The example shown in that chapter is a bit of an oversimplification, because it's a fixed-width histogram. There exists a more flexible type of histogram, called the variable-width histogram. This sort of graph is ideal for portraying the results of our hypothetical 40-question test given to 1000 students in various ways.

Figure 4-4 shows variable-width histograms that express the same data as that in the tables and pie graphs. In Fig. 4-4, graph A portrays the data results from Table 4-8, graph B portrays the results from Table 4-9, and graph C portrays the results from Table 4-10. The width of each vertical bar is directly proportional to the range of scores. The height of each bar is directly proportional to the percentage of students who received scores in the indicated range.

Percentages are included in the histogram of Fig. 4-4A, because there's room enough to show the numbers without making the graph look confusing or cluttered. In Figs. 4-4B and C, the percentages are not written at the top of each bar. This is a matter of preference. Showing the numbers in graph B would make it look too cluttered to some people. In graph C, showing the percentage for the grade of A would be difficult and could cause confusion, so they're all left out. It's a good idea to include tabular data with histograms when the percentages aren't listed at the tops of the bars.

## Fixed Intervals Practice Problems

#### Practice 1

Imagine a large corporation that operates on a five-day work week (Monday through Friday). Suppose the number of workers who call in sick each day of the week is averaged over a long period, and the number of sick-person-days per week is averaged over the same period. (A sick-person-day is the equivalent of one person staying home sick for one day. If the same person calls in sick for three days in a given week, that's three sick-person-days in that week, but it's only one sick person.) For each of the five days of the work week, the average number of people who call in sick on that day is divided by the average number of sick-person-days per week, and is tabulated as a percentage for that work-week day. The results are portrayed as a pie graph in Fig. 4-5. Name two things that this graph tells us about Fridays. Name one thing that this graph might at first seem to, but actually does not, tells us about Fridays.

#### Solution 1

The pie graph indicates that more people (on the average) call in sick on Fridays than on any other day of the work week. It also tells us that, of the total number of sick-person-days on a weekly basis, an average of 33% of them occur on Fridays. The pie graph might at first seem to, but in fact does not, indicate that an average of 33% of the workers in the corporation call in sick on Fridays.

#### Practice 2

Suppose that, in the above described corporation and over the survey period portrayed by the pie graph of Fig. 4-5, there are 1000 sick-person-days per week on average. What is the average number of sick-person-days on Mondays? What is the average number of people who call in sick on Mondays?

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