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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

Expert verified

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

Question: In his essay "Making Things Right," W. Edwards Deming considered the role of statistics in the quality control of industrial products. In one example, Deming examined the quality-control process for steel rods manufacturers. Rods produced with diameters smaller than 1 centimeter fit too loosely in their bearings and ultimately must be rejected (thrown out). To determine whether the diameter setting of the machine that produces the rods is correct, 500 rods are selected from the day's production, and their diameters are recorded. The distribution of the 500 diameters for one day's production is shown in the accompanying figure. Note that the symbol LSL in the figure represents the 1-centimeter lower specification limit of the steel rod diameters. There has been speculation that some of the inspectors are unaware of the trouble that an undersized rod diameter would cause later in the manufacturing process. Consequently, these inspectors may pass rods with diameters that are barely below the lower specification limit and record them in the intervalcenteredat 1.000 centimeters. According to the figure, is there any evidence to support this claim? Explain.

Discuss the conditions under which the median is preferred to the mean as a measure of central tendency.

Symmetric or skewed?Would you expect the data sets described below to possess relative frequency distributions that are symmetric, skewed to the right, or skewed to the left? Explain.

a.The salaries of all persons employed by a large university

b.The grades on an easy test

c.The grades on a difficult test

d.The amounts of time students in your class studied last week

e.The ages of automobiles on a used-car lot

f.The amounts of time spent by students on a difficult examination (maximum time is 50 minutes)

The amount spent on textbooks for the fall term was recorded for a sample of five university students. The following data were observed: \(400, \)350, \(600, \)525, and $450. Calculate each of the following values for this data:

a.The sample mean

b.The sample median

c.The sample range

d.The standard deviation

Explain how the relationship between the mean and median provides information about the symmetry or skewness of the data’s distribution.

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