The percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution can be determined using
A) Chebyshev's theorem.
B) The empirical rule.
C) A five-number summary.
D) Percentiles.

Question

​The percentage of data values that must be within one, two, and three standard deviations of the mean for data having a bell-shaped distribution can be determined using
A) ​Chebyshev's theorem.
B) The empirical rule.
C) ​A five-number summary.
D) ​Percentiles.

Quizplus · Accepted Answer

The empirical rule states that for data having a bell-shaped distribution, approximately 68% of the data values will be within one standard deviation of the mean, approximately 95% of the data values will be within two standard deviations of the mean, and approximately 99.7% of the data values will be within three standard deviations of the mean. Therefore, the best choice for determining the percentages of data values within one, two, and three standard deviations of the mean is the empirical rule.

​The Percentage of Data Values That Must Be Within One

The Percentage of Data Values That Must Be Within One