Answer the questions about variability of data sets.

a. What is the primary disadvantage of using the range to compare the variability of data sets?

A.

It is a sensitive measure of data variation.

B.

It is hard to compute.

C.

It does not have any units.

D.

It is a rather insensitive measure of data variation.

b. Describe the sample variance using words rather than a formula. Do the same with the population variance. Choose the correct answer below.

A.

The sample variance is the sum of the squared deviations from the mean divided by the number of measurements. The population variance is the sum of the squared deviations from the mean divided by the number of measurements minus one.

B.

The sample variance is the sum of the squared deviations from the mean divided by the number of measurements minus one. The population variance is the average of the squared distances of the measurements on all units in the population from the mean.

C.

The sample variance is the sum of the deviations from the mean divided by the number of measurements. The population variance is the sum of the deviations from the mean divided by the number of measurements minus one.

D.

The sample variance is the sum of the deviations from the mean divided by the number of measurements minus one. The population variance is the average of the distances of the measurements on all units in the population from the mean.

c. Can the variance of a data set ever be negative? Explain. Can the variance ever be smaller than the standard deviation? Explain.

A.

The variance of a data set cannot be negative because it is the sum of the squared deviations divided by a positive value. Variance can be smaller than the standard deviation if the variance is less than 1.

B.

The variance of a data set cannot be negative because deviation from the mean is always a positive value. Variance cannot be smaller than the standard deviation because the variance is the square of the standard deviation.

C.

The variance of a data set can be negative if the mean is negative. Variance can be smaller than the standard deviation if the variance is less than 0.

D.

The variance of a data set can be negative if all of the data values are negative. Variance cannot be smaller than the standard deviation because the standard deviation is the square root of the variance.

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