HW 2.4

Discuss the similarities and the differences between the Empirical Rule and​ Chebychev's Theorem.

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

What is an advantage of using the range as a measure of​ variation?

It is easy to compute.

What is a disadvantage of using the range as a measure of​ variation?

It uses only two entries from the data set.

What is a difference between the Empirical Rule and​ Chebychev's Theorem?

The Empirical Rule assumes the distribution is aproximately symmetric and​ bell-shaped and​ Chebychev's Theorem makes no assumptions.

Explain how to find the range of a data set

The range is found by subtracting the minimum data entry from the maximum data entry.

Explain the relationship between variance and standard deviation. Can either of these measures be​ negative? Explain.

The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Why is the standard deviation used more frequently than the​ variance?

The units of variance are squared. Its units are meaningless.

Describe the difference between the calculation of population standard deviation and that of sample standard deviation.

When calculating the population standard​ deviation, the sum of the squared deviation is divided by​ N, then the square root of the result is taken. When calculating the sample standard​ deviation, the sum of the squared deviations is divided by n−​1, then the square root of the result is taken.

Given a data​ set, how do you know whether to calculate σ or​ s?

When given a data​ set, one would have to determine if it represented the population or if it was a sample taken from the population. If the data are a​ population, then σ is calculated. If the data are a​ sample, then s is calculated.