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Explain why we generally prefer the standard deviation to the range as a measure of variability for quantitative data.

Short Answer

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The standard deviation tells us the variability of the data.

Step by step solution

01

Standard deviation

The variance or standard deviation of how much variance as well as dispersion there is in a group of numbers.A smaller standard deviation suggests that information is grouped around the mean, whereas a largestandard deviation showsthat observations are more dispersed.

02

Explaining the preference of standard Deviation over the range

The range is the difference between the maximum and the minimum value of the data set.It allows you to know the gap between the data set.

Standard Deviation tells us how far a particular value is from the data set's mean. It tells us how far the data is spread from the mean.

We generally prefer standard Deviation over the range because it allows us to understand the data set's variability. In contrast, the range only tells us the difference between the maximum and the minimum value.

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Most popular questions from this chapter

Consider the following sample of five measurements: 2, 1, 1, 0, 3.

a.Calculate the range, s2, and s.

b.Add 3 to each measurement and repeat part a.

c.Subtract 4 from each measurement and repeat part a.

d.Considering your answers to parts a, b, and c, what seems to be the effect on the variability of a data set by adding the same number to or subtracting the same number from each measurement?

Using only integers between 0 and 10, construct two data sets with at least 10 observations each that have the same range but different means. Construct a dot plot for each of your data sets, and mark the mean of each data set on its dot diagram.

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Compute xbar, s2, and sfor each of the following data sets. If appropriate, specify the units in which your answer is expressed.

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