Question

Chebyshev's theorem is applicable when the data are:

a) Normally distributed.
b) Skewed to the left.
c) Skewed to the right.
d) Any distribution.

Answer 1

Chebyshev's theorem is applicable to any distribution, ensuring minimum percentage of the data within a certain number of standard deviations from the mean, regardless of the data's distribution shape.

Step-by-step explanation:

Chebyshev's theorem applies to any distribution, which means it is not limited to data sets that are normally distributed or skewed in any particular direction. Chebyshev's theorem states that for any set of data, there are certain percentages that data will fall within a specified number of standard deviations from the mean. Specifically, at least 75 percent of the data is within two standard deviations of the mean, at least 89 percent is within three standard deviations, and at least 95 percent is within 4.5 standard deviations. This rule is true regardless of the shape of the data's distribution, which means it applies to normal, left-skewed, right-skewed, and any other type of distribution.