For any data set, regardless of its distribution, at least 75% of the data is within two standard deviations of the mean. This is a result of the Chebyshev's inequality, which states that for any real-valued random variable with a finite mean and standard deviation, the proportion of data that lies within \( k \) standard deviations of the mean is at least \( 1 - \frac{1}{k^2} \). For \( k = 2 \), this gives us at least \( 1 - \frac{1}{2^2} = 1 - \frac{1}{4} = 0.75 \) or 75%.
For any data set, regardless of the distribution, at least 75%
of the data is within how many standard deviations of the mean?
one
three
four
two
1 answer