When is standard deviation applicable in data analysis?

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. It is most applicable for continuous data, particularly when the data is normally distributed. This is because in a normal distribution, the standard deviation provides useful insights about the data's spread relative to the mean—specifically, it indicates how much individual data points typically deviate from the average.

In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations. This characteristic makes standard deviation a powerful tool for understanding variability in normally distributed datasets.

Using standard deviation for categorical (qualitative) data is inappropriate because such data is not numeric and does not have a meaningful way to measure dispersion. Standard deviation also doesn't apply accurately to continuous data that does not follow a normal distribution, as the interpretations become less meaningful outside of the normal curve's properties. Therefore, focusing on continuous data in a normal distribution is the proper context in which to apply standard deviation effectively.