According to Chebyshev's Theorem, at least what percent of the observations lie within plus and minus 1.75 standard deviations of the mean?
A) 56%
B) 95%
C) 67%
D) Cannot compute because it depends on the shape of the distribution

Question

Quizplus · Accepted Answer

Chebyshev's Theorem states that at least 1-1/k^2 of the observations lie within plus and minus k standard deviations of the mean. Plugging in k=1.75, we get 1-1/1.75^2 = 1-0.325 = 0.675 or 67.5%. However, since Chebyshev's Theorem gives a lower bound, it is possible that more than 67.5% of the observations lie within plus and minus 1.75 standard deviations of the mean.

According to Chebyshev's Theorem, at Least What Percent of the Observations