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What does a standard deviation of exactly zero tell you about a data set?
AThe mean of the data set is also zero
BThe data set holds only positive values
CThe data set has exactly two values in it
DEvery value in the set equals every other
Answer & Solution
Correct answer: D. Every value in the set equals every other
1. The standard deviation is zero or larger, never negative.
2. It reaches zero only when every squared deviation is zero.
3. That means every value sits exactly at the mean, so all the values are equal to each other.
4. The mean itself can be any number at all, so a zero deviation says nothing about its size.
_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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