Question

Discuss the similarities and the differences between the Empirical Rule and Chebychev's Theorem What is a similarity between the Empirical Rule and Chebychev's Theorem? 0 A. O B. ° C. Both apply only to symmetric and bell-shaped distributions. Both do not require the data to have a sample standard deviation. Both calculate the variance and standard deviation of a sample. D. 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 aproximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions O B. Chebychev's Theorem estimates proportions of data contained within infinite standard deviations and the Empirical Rule has a limit of 5 standard deviations ° C. The Empirical Rule assumes a small data set (less than 50 values) where Chebychev's Theorem has no limit on data size. O D. Chebychev's Theorem applies only to distributions which are approximately symmetric or bell-shaped and the Empirical Theorem has no restrictions.

Answer 1

Answer:

1. Option C

2. Option A

Step-by-step explanation:

We are given the following information in the question:

1. Similarity between the Empirical Rule and Chebychev's Theorem:

Both Empirical Rule and Chebychev's Theorem,  helps us to determine the percentage of data lying within the standard deviations from the mean value.

Hence, similarity is given by:

Option C)  Both calculate the variance and standard deviation of a sample.

2. Difference between the Empirical Rule and Chebychev's Theorem:

Empirical rule is applicable for normally distributed data and Chebychev's Theorem can be applied to any data.

Hence, the difference is given by:

Option A) The Empirical Rule assumes the distribution is approximately symmetric and bell-shaped and Chebychev's Theorem makes no assumptions.