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Chapter 3: Q 3.57. (page 113)
Explain the purpose of a measure of variation.
A measure of variation is a metric that shows how much variety or spread there is in a set of data.
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How many standard deviations to either side of the mean must we go to ensure that for any data set, at least of the observations lie within?
What does Chebyshev's rule say about the percentage of observations that lie within one standard deviation to either side of the mean? Discuss your answer.
In this exercise, you will compare Chebyshev's rule and the empirical rule.
a. Compare the estimates given by the two rules for the percentage of observations that lie within two standard deviations to either side of the mean. Comment on the differences.
b. Compare the estimates given by the two rules for the percentage of observations that lie within three standard deviations to either side of the mean. Comment on the differences.
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. ). 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
A quantitative data set has mean and standard deviation . At least what percentage of the observations lie between and
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