Statistics, Chapter 3

True or false: The variance is a measure of central tendency.

False

Which statement best describes the difference between the formula for Population and Sample variance?

For the sample variance, dividing by n-1 corrects a tendency to underestimate population variance.

What are reasons to study the dispersion of data?

It allows us to compare the spread in two or more distributions. A small value for dispersion indicates that the data is closely clustered around the center.

What is an advantage of the range compared to the variance?

It is simpler to understand and calculate.

What are the weaknesses of the range as a measure of dispersion?

It may be unduly influenced by an unusually large value It may be unduly influenced by an especially small value. Only two values from the data set are used.

What does a measure of dispersion tell us about a set of data?

It tells us about the spread of the data.

Which of the following are advantages of the variance compared to the range?

It uses all of the values in the data, not just two. It is not unduly influenced by large or small values.

What are the reasons why the mode would not be a good choice of measure for the describing the center of a set of data?

The data is bimodal. The most frequent observation is much higher or much lower than most of the data values.

True or false: The standard deviation is a measure of dispersion

True

What is the strength of the range as a measure of dispersion?

It is easy to calculate

Chebyshev's Theorem states that the proportion of values is at least 1-1/k2. What is the meaning of k?

k is the number of standard deviations, greater than 1, within which that proportion of observations will be found.

The larger the population variance is for a data set,

the more spread out the data is

What is true regarding the application of Chebyshev's theorem and the Empirical Rule?

Chebyshev's theorem works for symmetrical, bell-shaped distributions. Chebyshev's theorem applies to any set of values.

What does n represent in the formula for the sample variance?

The sample size

What is an advantage of the standard deviation over the variance?

It is in the same units as the data.

What does N represent in the formula for the population variance?

The number of observations in the population

Which statement is true with regard to differences in the formula for the population and samples variances?

The sample variance measures deviations from the sample mean, whereas the population variance uses the population mean.

Which measure of dispersion results in units that are different from the data?

Variance