Definition
Standard deviation is a statistical measure of how spread out data points are from the mean. A larger value indicates greater variability. It is defined as the positive square root of the variance, which is the average of the squared differences from the mean.
Relationship with Normal Distribution
When data follows a normal distribution, approximately 68% falls within one standard deviation of the mean, 95% within two, and 99.7% within three. This is known as the 68-95-99.7 rule and provides a quick way to assess how unusual a particular value is.
Use in Rankings
For data that approximates a normal distribution, such as height, standard deviation enables efficient percentile calculation. By determining how many standard deviations a value is from the mean (the z-score), the corresponding percentile can be derived from the normal distribution table.
However, for data that does not follow a normal distribution, such as income, standard deviation alone cannot adequately describe the shape of the distribution. MyRank selects appropriate calculation methods based on each indicator's distributional characteristics.
Practical Interpretation
Understanding standard deviation helps you gauge whether your position in a ranking is typical or exceptional. Being two standard deviations above the mean places you roughly in the top 2.5% of a normally distributed population.