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.

Explanation:

The Empirical Rule gives approximate proportions of data within 1, 2, and 3 standard - deviations of the mean for a normal (symmetric and bell - shaped) distribution. Chebychev's Theorem gives a lower bound for the proportion of data within k standard deviations of the mean for any distribution. The key similarity is that they both estimate proportions of data within k standard deviations of the mean.

Answer:

B. Both estimate proportions of the data contained within k standard deviations of the mean.