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Whatever the shape of the data, at least what share of it lies within two standard deviations of the mean?
AAt least 68 percent of the data
BAt least 75 percent of the data
CAt least 89 percent of the data
DAt least 95 percent of the data
Answer & Solution
Correct answer: B. At least 75 percent of the data
1. This guarantee holds for any data set, whatever its shape.
2. Within two standard deviations of the mean it promises at least 75 percent of the data.
3. Three standard deviations raise the guarantee to at least 89 percent.
4. The figure of 68 percent belongs to the rule for bell-shaped data at one standard deviation, not to this general guarantee.
_Source: OpenStax Introductory Business Statistics (CC BY 4.0), Ch 2 "Descriptive Statistics", section 2.7 Measures of the Spread of the Data_
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