5) Explain why the median is often preferred to the mean as a measure of central

Question

5) Explain why the median is often preferred to the mean as a measure of central tendency for a skewed distribution.

6) Schmidt (1994) conducted a series of experiments examining the effects of humor on memory. In one study, participants were shown a list of sentences, of which half were humorous and half were nonhumorous. A humorous example is, “If at first you don’t succeed, you are probably not related to the boss.” Other participants would see a nonhumorous version of this sentence, such as “People who are related to the boss often succeed the very first time.”

Schmidt then measured the number of each type of sentence recalled by each participant. The following scores are similar to the results obtained in the study.

4 5 2 4 5 2 4 2   

6 7 6 6 2 3 1 6

2 5 4 3 3 2 3 3

1 3 5 5 4 1 5 3

4 5 2 4 5 2 4 2   

6 7 6 6 2 3 1 6

2 5 4 3 3 2 3 3

1 3 5 5 4 1 5 3

Explanation / Answer

5) Often introductory applied statistics texts distinguish the mean from the median (often in the the context of descriptive statistics and motivating the summarization of central tendency using the mean, median and mode) by explaining that the mean is sensitive to outliers in sample data and/or to skewed population distributions, and this is used as a justification for an assertion that the median is to be preferred when the data are not symmetrical.

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