Question

compare chebyshevs rule and the empirical rule.
a. compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. comment on the differences.
b. compare the estimates given by the two rules for the percentage of observations that lie within three standard deviations to either side of the mean. comment on the differences.
a. compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. comment on the differences.
using chebyshevs rule, find the estimate for the percentage of observations that lie within two standard deviations to either side of the mean.
at least 75% of the observations in any data set lie within 2 standard deviations to either side of the mean. (type an integer or a decimal. do not round.)
using the empirical rule, find the estimate for the percentage of observations that lie within two standard deviations to either side of the mean.
approximately 95% of the observations in any data set lie within 2 standard deviations to either side of the mean. (type an integer or a decimal. do not round.)
select the best answer that describes the differences in the two rules.
a. chebyshevs rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area.
b. chebyshevs rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. in this case, chebyshevs rule captures more of the observations in the area.
c. chebyshevs rule is for any quantitative data set and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for a data set that is roughly bell shaped and gives the percentage that approximates the number of observations that could be included in the area. in this case, the empirical rule captures more of the observations in the area.
d. chebyshevs rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area. the empirical rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. in this case, the empirical rule captures more of the observations in the area.

Explanation:

Chebyshev's rule applies to any quantitative data - set and gives the percentage of the least number of observations that could be included in a certain number of standard - deviations from the mean. The empirical rule applies to roughly bell - shaped data sets and gives the percentage of observations that are definitely included in a certain number of standard - deviations from the mean. In the case of two standard - deviations from the mean, Chebyshev's rule gives a lower bound estimate and the empirical rule gives a more precise estimate for bell - shaped data.

Answer:

B. Chebyshev's rule is for any quantitative data set and gives the percentage that approximates the number of observations that could be included in the area. The empirical rule is for a data set that is roughly bell shaped and gives the percentage of the least number of observations that are definitely included in the area.