Statistics · BEGINNER LESSON
Standard deviation
Standard deviation is a measure of spread that shows how far data values are from their mean. It is computed from squared differences from the mean, then square-rooted, and it is always zero or positive.
What it is
Standard deviation, often shortened to SD, is a basic measure of variability in a set of numbers. It summarizes how far the values usually sit from the mean, which is the average of the data. If the SD is small, the values are clustered near the mean; if it is large, the values are more spread out. The usual sample formula uses n−1 in the denominator, while a population formula uses N. [sourceIndexes: 1,2]
[2] When means and standard deviations are an incomplete ... [3] 13.2 Measures of Spread - Principles of Finance 2e | OpenStax
How it is calculated
To compute sample SD, first find the mean. Then subtract the mean from each value, square each difference, add the squared differences, divide by n−1, and take the square root. Squaring makes all differences positive, and the square root returns the result to the original units. The same framework underlies variance, which is the squared form of SD. [sourceIndexes: 2]
[3] 13.2 Measures of Spread - Principles of Finance 2e | OpenStax
What it tells you
SD is commonly used because it gives a single number for overall spread around the mean. It can help show whether values are tightly packed or widely scattered. In some applications, such as blood pressure variability, SD is used as a fundamental metric for overall variability around the mean. [sourceIndexes: 0,1]
[1] Table 1. [2] When means and standard deviations are an incomplete ...
Limits and cautions
SD is sensitive to outliers, meaning unusual extreme values can pull it upward. It also does not by itself describe skewed data well, because a non-normal distribution may need other summaries such as the median and interquartile interval. For skewed data, SD may still be useful, but it should not be the only summary reported. [sourceIndexes: 0,1]
[1] Table 1. [2] When means and standard deviations are an incomplete ...
SEE THE IDEA
How standard deviation is obtained
Start with the observed numbers in a sample or population.
Find the average; this is the center used for comparison.
Subtract the mean from each value, then square the differences.
Average the squared differences and take the square root to get SD.
Each step transforms raw values into one measure of spread around the mean.
Standard deviation is built from distances from the mean, with squaring and square-rooting to keep the final measure usable.
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.