Question

discuss the similarities and the differences between the empirical rule and chebychevs theorem.
what is a similarity between the empirical rule and chebychevs theorem?
a. both apply only to symmetric and bell - shaped distributions.
b. both estimate proportions of the data contained within k standard deviations of the mean.
c. both calculate the variance and standard deviation of a sample.
d. both do not require the data to have a sample standard deviation.
what is a difference between the empirical rule and chebychevs theorem?
a. the empirical rule assumes the distribution is aproximately symmetric and bell - shaped and chebychevs theorem makes no assumptions.
b. chebychevs theorem applies only to distributions which are approximately symmetric or bell - shaped and the empirical theorem has no restrictions.
c. the empirical rule assumes a small data set (less than 50 values) where chebychevs theorem has no limit on data size.
d. chebychevs theorem estimates proportions of data contained within infinite standard deviations and the empirical rule has a limit of 5 standard deviations.

Explanation:

The Empirical Rule and Chebychev's Theorem are both statistical tools. The similarity is that they estimate data - proportion within k standard deviations of the mean. The key difference is that the Empirical Rule applies to symmetric and bell - shaped distributions while Chebychev's Theorem has no such distributional assumptions.

Answer:

What is a similarity between the Empirical Rule and Chebychev's Theorem?
B. Both estimate proportions of the data contained within k standard deviations of the mean.
What is a difference between the Empirical Rule and Chebychev's Theorem?
A. The Empirical Rule assumes the distribution is approximately symmetric and bell - shaped and Chebychev's Theorem makes no assumptions.