I have been racking my brain around standard deviation. I came to the conclusion it being a measurement of scores that entails a range of high or low due to the scores or variables. My question is: Why normality is required for standard deviation applicability?

As long as the distribution is normal, the SD cuts off particular percentages. As the distribution deviates from normal, these percentages no longer apply.

Thank you

To understand why normality is required for the applicability of standard deviation, we need to delve into the concept of standard deviation itself.

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a dataset. It tells us how spread out the individual values or scores are from the mean (average). In simpler terms, standard deviation provides information about the average distance between each data point and the mean.

Normality, on the other hand, refers to the shape of the distribution of data points in a dataset. A normal distribution, also known as a bell curve, is characterized by a symmetrical shape with a peak at the mean and a decline towards the tails. Many real-world phenomena, such as height or test scores, tend to follow a normal distribution.

Now, why is normality required for the applicability of standard deviation? The answer lies in the mathematical properties of the standard deviation formula. The formula assumes that the data follows a normal distribution, which enables accurate calculation and interpretation of the standard deviation.

When the data is normally distributed, the standard deviation can be used to make certain assumptions about the data. For example, we can say that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. These assumptions hold true when dealing with normally distributed data, and they form the basis for many statistical analyses and inferences.

However, in cases where the data deviates significantly from a normal distribution, the assumptions underlying standard deviation calculations may not hold. This can lead to incorrect interpretations or misleading results. Therefore, normality of the data is a prerequisite for reliably applying and interpreting standard deviation measures.

It's worth mentioning that even when dealing with non-normally distributed data, standard deviation can still be calculated and provide some information about the dispersion in the dataset. However, in such cases, alternative statistical measures or techniques may need to be considered to properly analyze the data.

In summary, normality is required for the applicability of standard deviation because the formula and assumptions underlying standard deviation calculations are based on the properties of normally distributed data.