Explain why normality is required for standard deviation applicability. Please give examples.
Normal is important because what we are statistically after is a mean that is statistically significant when we say that the average height of a US man is such and such and the average height of a US woman is this. We would be able to statistically validate that the largest percentage of heights is within set standard deviations from the average height. Our curve would be statistically significant and reliable in determining the height of men and women in the US.
If however our sample departed from the norm and we included an abnormally large sample of individuals who are 7' and taller or 4' and shorter our mean or average height would not be statistically significant in determining the true average height of men and women in the US. The mean would be either too tall or too short because of using an abnormal sample. Standard ...
The standard deviation applicability normality is examined. Examples are provided.