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Chapter 3: Q. 2 (page 150)

Identify the two most commonly used measures of center for

quantitative data. Explain the relative advantages and disadvantages

of each.

Short Answer

Expert verified

The two most commonly used measures of center for quantitative data is mean and median.

The median is not sensitive to extreme data while the mean is sensitive.

When the data set is qualitative, neither the mean nor the median is adequate to measure the center.

Step by step solution

01

Part a. Two most common measures of center

Mean and Median are two most commonly used measures of center for quantitative data.

02

Part b. Merits and Demerits of Mean and Median.

The median is not sensitive to extreme data while the mean is sensitive.

For extreme observation, the median is selected over the mean.

When the data is qualitative, it is impossible to add or divide the values.

When the data is qualitative, it is impossible to assign a numerical order to the data set. If data is qualitative, the median is not an acceptable metric.

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Most popular questions from this chapter

Floor space: The U.S department housing and urban development compiles information on new, privately owned single family houses. According to the document in 2012 the mean floor space of such homes are2505sqftand the median was2306sqft. Which measure of center do you think is more appropriate? Justify your answer.

The Etruscans. Anthropologists are still trying to unravel the mystery of the origins of the Etruscan empire, a highly advanced Italic civilization formed around the eighth century B.C. in central Italy. Were they native to the Italian peninsula or, as many aspects of their civilization suggest, did they migrate from the East by land or sea? The maximum head breadth, in millimeters, of 70 modern Italian male skulls and that of 84 preserved Etruscan male skulls were analyzed to help researchers decide whether the Etruscans were native to Italy. The resulting data can be found on the WeissStats site. [SOURCE: N. Barnicot and D. Brothwell, "The Evaluation of Metrical Data in the Comparison of Ancient and Modern Bones." In Medical Biology and Etruscan Origins, G. Wolstenholme and C. O'Connor, cds., Littlc, Brown \& Co., 1959]

Discuss the pros and cons of Chebyshev's rule.

Is an extreme observation necessary an outlier? Explain your answer.

Treating Psychotic Illness. L. Petersen et al evaluated the effects of integrated treatment for patients with a first episode of psychotic illness in the paper "A Randomized Multicenter Trial of Integrated Versus Standard Treatment for Patients with a First Episode of Psychotic Illness" (British medical journal, vol. 331.(7517):602). Part of the study included a questionnaire that was designed to measure client satisfaction with both the integrated treatment and standard treatment. The data on the Weiss Stats site is based on the results of the client questionnaire.

(a) Use the technology of your choice to obtain boxplots for the data sets, using the same scale.

(b) Compare the data sets by using your results from part(a) paying special attention to center and variation
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