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## STAT200 Southern Illinois University Standard Deviation Discussion

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InstructionsSTAT200 Southern Illinois University Standard Deviation Discussion

Question Description

This week, we are covering an important concept that is widely used in a variety of fields: the standard deviation. The standard deviation is a measure of how close together a set of data isgrouped. In Chapter 2 of your text, Kozak (2014) stated:

In general a small standard deviation means the data is close together (more consistent) and a large standard deviation means the data is spread out (less consistent). Sometimes you

want consistent data and sometimes you dont. As an example if you are making bolts, you want to lengths to be very consistent so you want a small standard deviation. If you are

administering a test to see who can be a pilot, you want a large standard deviation so you can tell who are the good pilots and who are the bad ones. (p. 89).

Example Situations Involving Pilots

A large standard deviation tells us that there is a lot of variability in the scores; that is, the distribution of scores is spread out and not clustered around the mean. As Kozak (2104) has stated, when assessing potential pilots, we may want a large standard deviation, so that we can differentiate between candidates; that is, we can determine who would be good pilots and those who

would not be good pilots. Since a large standard deviation tells us that there is a lot of variability in the scores, candidates, who would be good pilots, would have scores far above the mean,

while those who would not be good pilots would have scores far below the mean. Thus, only the “top” candidates would be selected to be pilots.

A small standard deviation tells us that there is not a lot of variability in a distribution of scores; that is, the scores are very consistent (similar) and close to the mean. Using our pilot example, a small standard deviation is desirable, when considering aircraft landing distances. If there is not enough distance when landing, the aircraft could undershoot the runway; that is, land short of

the runway. On the other hand, if there is too much distance, the aircraft can overshoot the runway; that is, the aircraft does not stop before the end of the runway. Both undershooting and

overshooting runways could result in injuries and/or fatalities. Thus, it is important that pilots have consistent accurate landing distances. Specifically, over a number of landings, the distances would, on average, be appropriate to the runway length with little variation among the distances.

Now think about how this might apply in your chosen field and answer both of the following questions:

What is an example of when you would want consistent data and, therefore, a small standard deviation?

What is an example of when you might want a large standard deviation? That is, data that is more spread out?

Reference

Kozak, K. (2014). Statistics using technology. Retrieved from https://s3-us-west-2.amazonaws.com/oerfiles/statsusingtech.pdf

RUBRIC

Excellent Quality95-100%

Introduction45-41 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Literature Support91-84 points

The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.

Methodology58-53 points

Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.

Average Score50-85%

40-38 points

More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.

83-76 points

Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.

52-49 points

Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.

Poor Quality0-45%

37-1 points

The background and/or significance are missing. No search history information is provided.

75-1 points

Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.

48-1 points

There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met

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STAT200 Southern Illinois University Standard Deviation Discussion

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