Definition
Standard deviation is a measure of how spread out the values in a dataset are relative to the mean. A low standard deviation means most values are close to the average, while a high standard deviation means the values are more widely scattered.
How It Works
To calculate standard deviation, you find how far each value is from the mean, square those differences, average them (giving you the variance), and then take the square root to return to the original units.
Two classes take the same test. Both have a mean score of 75.
Class A scores: 73, 74, 75, 76, 77 - Standard deviation = 1.4
Class B scores: 50, 60, 75, 90, 100 - Standard deviation = 18.7
Class A students performed very similarly. Class B had a wide range of performance. The standard deviation captures this difference.
Why It Matters
Standard deviation is one of the most important numbers in statistics. It appears in confidence intervals, hypothesis tests, quality control, and finance. When a financial analyst says a stock is "volatile," they are often referring to a high standard deviation in its returns.
In a normal distribution, about 68% of values fall within one standard deviation of the mean, and about 95% fall within two. This "68-95-99.7 rule" makes standard deviation a powerful tool for understanding what is typical and what is unusual.
Standard deviation quantifies variability. Pair it with the mean to understand both the center and the spread of your data.