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When does the rule about 68 percent, 95 percent and 99 percent of the data apply?
AOnly when the sample holds at least 100 values
BOnly when the data have been grouped into classes
COnly when the data set contains no outlier at all
DOnly when the shape is bell-shaped and symmetric
Answer & Solution
Correct answer: D. Only when the shape is bell-shaped and symmetric
1. The 68, 95 and 99 percent figures are read off a normal curve.
2. They therefore hold only when the data are bell-shaped and symmetric.
3. For any other shape the weaker general guarantee of at least 75 percent within two standard deviations must be used instead.
4. Sample size alone does not make a distribution normal, so a count of 100 values is not the condition.
_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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