Instruction
Need this question done in a paragraph.....
Standard deviation is introduced in Chapter 8 (Measuring Variability), and used in Chapter 9 (Probability and Normal Curve).
Standard deviation is a descriptive statistic that is used to understand the distribution of a dataset. It is often reported in combination with the mean (or average), giving context to that statistic. Specifically, a standard deviation refers to how much scores in a dataset tend to spread-out from the mean.
A small standard deviation (relative to the mean score) indicates that the majority of individuals (or data points) tend to have scores that are very close to the mean. In this case, cases may look clustered around the mean score, with only a few scores farther away from the mean (probably outliers).By contrast, a sample with a large standard deviation (relative to the mean score) tends to have cases that are more widely spread-out from the mean, perhaps with only a few cases actually having scores that fall close to the mean.
You may be wondering to yourself: "Why should I care about the standard deviation?" The answer to that question is context. To really understand the basic characteristics of a dataset, you must put your statistics in context.
For example, if I want to wade across a river that on average is 3 feet deep, I'd like to know that the standard deviation around that mean (average) is small. This would imply the river bottom is relatively flat. But if someone told me that the standard deviation around that 3 foot average was high (say, a standard deviation of 3 feet), I would know as I waded across that I could be stepping into some fairly large holes!
Provide some examples of datasets that might have small standard deviations, and others that might have large standard deviations.