Mathematics Homework Help

Implications of Difference in Standard Deviation Size

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 is grouped. 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 don’t. 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