LydiaLe@UTS-Learning Arguments-Evidence and Intuition

Standard Deviation

PART 1

What is standard deviation?

In terms of central tendency of a data set, Virginia Tech (2006) defines the Standard Deviation as a measure of dispersion describing the spread of scores around the mean. It is considered as the most common measure of the spread of data distribution and is a computed measure of how much scores vary around the mean score. In other words, standard deviation is a measure of how much scores differ or vary from the mean of the scores.

In addition a picture of numbers, Math Fun Advanced (2014) states that the Standard Deviation is a measure of how spread out the numbers are.

In graphs, Standard Deviations are visually illustrated through curves. The following is the normal curve, from the Business Insider Australia (2016), showing a picture of Standard Deviations.

According to the Business Insider (2016), there are three standard deviations of the mean namely one standard deviation of the mean, two standard deviations of the mean, and three standard deviations of the mean. Further in detail, it also indicates that 68% of the data are within one standard deviation, 95% of the data are within two standard deviations, and 99,7% of the data are within three standard deviations. See a figure 1

Source from the Business Insider Australia (2016). Available at http://www.businessinsider.com.au/standard-deviation-2014-12?r=US&IR=T

Figure 1: The normal curve of three standard deviations of the mean.

Why does Standard Deviation matter?

The importance of standard deviation is that it is considered as the first cousin of the mean because when researchers report the average or mean they usually report standard deviation (Quizlet, 2016).

In addition, standard deviation is crucial because as mentioned, it is a measure of how spread out a data set is, therefore the locations of cores are determined. In other words, standard deviation is a measure of how far away individual measurements tend to be from the mean value of a data set (Business Insider Australia, 2016),

Further, in terms of comparisons and decision making, it is believed that without standard deviations, two or more data sets can not be effectively compared (Dummies, 2016), hence the decisions are not logically made.

Importantly, in reality things are surrounded by a vast of uncertainty, and in order to make effectively decisions, the uncertainty needs to be measured. According to the Explorable (n.d.) standard deviation is a best tool for the measurement of uncertainty. In a similar view with the mentioned importance, Exploreable agrees that the standard deviation fundamentally tells us about how the data is distributed about the mean value.

References and useful links