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.

What does standard deviation measure? In looking at the standard deviations of the "with fireplace" and "without fireplace" selling prices, one is much larger than the other. What could cause the standard deviations to be so different?

Returns for the Shields Company over the last 3 years are shown below. What's the standard deviation of Shields' returns? (Hint: This is a sample, not a complete population, so the sample standard deviation formula should be used.)
Year
Return
2006
2

Two craps tables collect an average of $500 per hour. One table has a standard deviation of $50 while the other has a standard deviation of $150. What conclusion can be drawn from the data? Normally, would one want a larger of smaller standard deviation? Please discuss and show any work associated with this question. Thanks

The score distribution shown in the table is for all students who took a yearly AP stats exam.
Score Percent of Students
5 13.3
2 21.9
3 24.9
2 17.8
1 22.1
Find the meanAND standard deviation:

Use the data below to answer the determine variance and standard deviation. (note: carry your calculator out to 4 decimal places).
Year Actual Return Average Return Deviation for the Mean Squared Deviation
1 .12 .103 .017

To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below:
$ 298 $ 125 $ 511 $ 157 $ 231 $ 230 $ 304 $ 372
Find the Standard deviation

1.) Test one: mean is 80 and standard deviation is 9. Mark scores 91
Test two: mean is 77 and standard deviation is 6. Mark score 87
Find the percentile for all
Which test Mark did better? Why?
2.) What is the the standard deviation for IQ tests? If someone's IQ is 140, how many standard deviation is it above the