Introduction
Standard deviation is a statistical measure used to tell how a given data is spread out from the mean or average. If the standard deviation for a given set of data is low, it means that most of the data in the given set are very close to the mean (Kozak, 2014). On the other hand, a high standard deviation means that the data in the given set of measurement are spread out (Kozak, 2014). The standard deviation of a given set of data is calculated by first computing the difference of each given measurement from the average and then squaring each result. The mean of these values is then determined, and then the square root is taken. The result obtained is the standard deviation of the given set of data. This paper gives an example of when an individual would want consistent data, hence, a small standard deviation as well as when an individual might want a more spread out data, hence, a large standard deviation.
Example of when one Might need Consistent Data (Smaller Standard Deviation)
In certain situations, such in product manufacturing and quality control where the results are restricted, a small standard deviation can be the goal. For instance, in a car manufacturing firm, when designing a specific part of a car part that ought to be 5 centimeters in length or diameter to fit in a given part properly ought not to have a large standard deviation when manufacturing that part of the car. In this case, a small standard deviation would mean that the part of the car fits properly; either that or the cars will not have problems down the road. On the other hand, a large standard deviation would mean that numerous parts of the material used would end up in the trash since their parts do not fit properly. This might lead to either that part or the cars to have problems down the road.
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Example of when one Might need spread Out Data (Larger Standard Deviation)
There are certain situations where one may need a large standard deviation, for instance, when one wants to determine who is a good race-car driver among many race-car drivers. To determine this, a standard race with many race-cars as well many race-car drivers ought to be conducted on various tracks. A larger standard deviation means that the individual performance of the numerous race-car driver is spread out. Since the data is spread out, it means that some of the race-car drivers outperform others. Thus, it is easier to find the best race car drivers when the standard deviation is large compared when the standard deviation is small. Through this, a driver who knows how to race as well as understands all the fundamentals of racing or driving can be selected.
Conclusion
As seen in the above two scenarios, there are certain situations when one might need a smaller standard deviation as well as scenarios where one might need a larger standard deviation. This statistical measurement of variability is very popular since it returns to the respective units data set measured. The more consistent a data distribution is the smaller its standard deviation and vice versa. There are potentially limitless situations where an individual might need to use either small or large standard deviations. Apart from expression variability, the standard deviation is also used to determine the confidence interval (CI) in statistical conclusions. This is what makes standard deviation a good as well as a popular statistical measure of variability.
References
Kozak, K. (2014). Statistics Using Technology. [Online]. Available at: https://s3-us-west-2.amazonaws.com/oerfiles/statsusingtech.pdf . Accessed 23 rd Jan 2019.
