3-2 Measures of Variation 105 ■ Both data sets have the same mean of 12.2 ounces. ■ The two data sets have very different amounts of variation, as indicated by the dramatically different amounts of spread in the two histograms and the dramatically different amounts of spread in the two dotplots. (Compare the two dotplots to see that the points in the dotplot of regular Coke volumes are very close together, but the points in the dotplot of Special Cola volumes are spread much farther apart.) FIGURE 3-3 Volumes of Regular Coke and Special Cola The volumes of regular Coke appear to vary very little about the mean of 12.2 oz, but the volumes of Special Cola appear to vary substantially about the mean of 12.2 oz. Continuing production of the Special Cola with such excessive variation would eventually result in disaster for the Special Cola company. It is likely that the company would not be able to stay in business with such a poor product. Consequently, companies often have this important goal: Improve quality by reducing variation in goods and, or services. We can subjectively compare the variation in the volumes of cola illustrated in Figure 3-3, but this concept of variation is so critically important that we need objective measures instead of relying on subjective judgments. We will now proceed to consider such measures of variation. To keep our round-off rules as consistent and as simple as possible, we will round the measures of variation using this rule, which is the same round-off rule used for the mean, median, and midrange: ROUND-OFF RULE FOR MEASURES OF VARIATION When rounding the value of a measure of variation, carry one more decimal place than is present in the original set of data.
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