Chebyshev’s Rule and the Empirical Rule are useful as a check on the calculation of the standard deviation. For example, suppose we calculated the standard deviation for the R&D percentages (Table 2.6)  to be 3.92. Are there any “clues” in the data that enable us to judge whether this number is reasonable?

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Table 2.6 R&D Percentages for 50 Companies 13.5 7.2 9.7 11.3 8.0 9.5 7.1 7.5 17557 51661 5.6 7.4 8.2 9.0 7.2 10.1 10.5 6.5 9.9 5.9 8.0 7.8 8.4 8.2 6.6 8.5 7.9 8.1 13.2 11.1 11.7 6.5 6.9 9.2 8.8 7.1 6.9 7.5 6.9 5.2 7.7 6.5 10.5 9.6 10.6 9.4 6.8 13.5 7.7 8.2 6.0 9.5