3.2 Measures of Dispersion Homework

What is the similarity between the Empirical Rule and Chebychev's Theorem?

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

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

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

In a statistics class, the standard deviation of the heights of all students was 4.2 inches. The standard deviation of the heights of males was 3.3 inches and the standard deviation for the females was 3.2 inches. Why is the standard deviation of the entire class more than the standard deviation of the males and females considered separately?

The distribution of the entire class has more dispersion

What makes the range less desirable than the standard deviation as a measure of dispersion?

The range does not use all the observations.

What is meant by the phrase " degrees of freedom" as it pertains to the computation of the sample standard deviation?

There are n-1 degrees of freedom in the computation of s because an unknown parameter, u, is estimated at x (x should have a line above it). For each parameter estimated, 1 degree of freedom is lost.

True or false: Chebyshev's inequality applies to all distributions regardless of shape, but the empirical rule holds only for distributions that are bell shaped.

True, Chebyshev's inequality is less precise than the empirical rule, but will work for any distribution, while the empirical rule only works for bell-shaped distributions.

True or false: When comparing two populations, the larger the standard deviation, the more dispersion the distribution has, provided that the variable of interest from the two populations has the same unit of measure.

True, because the standard deviation describes how far, on average, each observation is from the typical value. A larger standard deviation means that observations are more distant from the typical value, and therefore, more dispersed.

The standard deviation is used in conjunction with the ______ to numerically describe distributions that are bell shaped. The ______ measures the center of the distribution, while the standard deviation measures the ______ of the distribution.

mean, mean, spread