Question

What does Chebyshev’s theorem state and how can it be used in practice?

Answer 1

Chebyshevs Theorem: For any set of data (either population or sample) and for any constant k greater than 1, the proportion of the data that must lie within k standard deviations on either side of the mean is atleast 1 -1/k²

Example

Each year the National Weather Bureau produces information on the number of hurricanes in the U.S. The total number of hurricanes reported globally between the years of 1980 and 2006 are as follows:

75 79 83 86 71 44 86 77 87 100 94 66 40 72 61 42

Calculate the sample mean and sample standard deviation.

Use Chebyshevs Theorem to find an interval centered about the mean in which you would expect 75% of the years to fall.

Use Chebyshevs Theorem to find an interval centered about the mean in which you would expect 88.9% of the years to fall.

Use Chebyshevs Theorem to find an interval centered about the mean in which you would expect 96% of the years to fall.