The empirical rule, or the 68-95-99.7 rule, tells you where your values lie: The standard deviation and the mean together can tell you where most of the values in your distribution lie if they follow a normal distribution. The curve with the lowest standard deviation has a high peak and a small spread, while the curve with the highest standard deviation is more flat and widespread. The standard deviation reflects the dispersion of the distribution. However, their standard deviations ( SD) differ from each other.
The mean ( M) ratings are the same for each group – it’s the value on the x-axis when the curve is at its peak. Example: Comparing different standard deviationsYou collect data on job satisfaction ratings from three groups of employees using simple random sampling. When you have the standard deviations of different samples, you can compare their distributions using statistical tests to make inferences about the larger populations they came from. Many scientific variables follow normal distributions, including height, standardized test scores, or job satisfaction ratings. The standard deviation tells you how spread out from the center of the distribution your data is on average. Most values cluster around a central region, with values tapering off as they go further away from the center. In normal distributions, data is symmetrically distributed with no skew. Standard deviation is a useful measure of spread for normal distributions.
Standard deviation formulas for populations and samples.
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