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Mean and Standard Deviation

The claim has been made that the mean and the standard deviation are the most important measures of location and dispersion in statistics. Some commentators claim that these measures are more important than other measures such as median, mode or mean deviation.

QUESTIONS:

Why the emphasis on mean and standard deviation rather than other measures?

Do you agree or disagree? What reasons are available to support your answers?

Solution Preview

Interesting discussion question. Let's take a closer look. I also attached one resource to consider.

RESPONSE:

1. The claim has been made that the mean and the standard deviation are the most important measures of location and dispersion in statistics. Some commentators claim that these measures are more important than other measures such as median, mode or mean deviation. Do you agree or disagree? What reasons are available to support your answers?

The mean and standard deviation are the most important measures of location and dispersion when the assumptions of the normal distribution hold true in inferential statistics. A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other. (2)

(1) Standard Deviation and Mean are mathematically tractable

For example, the standard deviation formula is very simple: it is the square root of the variance. It is the most commonly used measure of spread.

First, an important attribute of the standard deviation as a measure of spread, and thus important in statistics, is that if the mean and standard deviation of a normal distribution are known, it is possible to compute the percentile rank associated with any given score. Thus, the mean and standard deviation are important in ...

Solution Summary

This solution discusses in some detail the following debate question: Why the emphasis on mean and standard deviation rather than other measures. Supplemented with a resource describing the measures of central tendencies.

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