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Chapter 2: Q56E (page 103)

Answer the following questions about the variability of data sets:

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

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

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

Short Answer

Expert verified

a) Same range but different data variation

b) Sample variance is the squared summation of the differences in observations from the mean divided by the number of observations minus one. Population variance is the summation of squared differences from the mean divided by the total number of observations.

c) No, the variance can never be negative. Yes, the variance can be smaller than the standard deviation.

Step by step solution

01

Disadvantage of using range to compare data variation

It is not advisable to use range to compare data variation because the range might be the same for two data sets. Still, there might be a very significant difference in the variation of the data.

For example, the range of heights in two groups of students may be the same, but there are chances that the height of students in group 1 is spread out symmetrically, and the height of students in group 2 is concentrated to the right.

02

Describing sample variance and population variance in words.

Sample variance is the squared summation of the differences of observations from the mean divided by the number of observations minus one.

Population variance is the summation of squared differences from the mean divided by the total number of observations.

03

Variance of a data set ever be negative or not

No, the variance cannot be negative because it is the square of deviations from the mean. And based on the basic mathematic rules, a square can never be negative.

The variance can be smaller than the standard deviation when the observations range between 0 and 1.

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