Standard deviation measures the amount of variation or dispersion of a set of data points relative to their mean (average). Specifically, it quantifies how spread out the data are around the mean:
- A low standard deviation means the data points are clustered closely around the mean, indicating less variability.
- A high standard deviation means the data points are more spread out over a wider range of values, indicating greater variability
It is calculated as the square root of the variance, which is the average of the squared differences from the mean. Standard deviation is expressed in the same units as the data, making it intuitive to interpret
. In practical terms, standard deviation helps determine how typical or unusual a particular data point is within a dataset. For example, in a normally distributed dataset, about 68% of values lie within one standard deviation of the mean, 95% within two, and 99.7% within three standard deviations
. In summary, standard deviation measures how much individual data points deviate, on average, from the mean, reflecting the overall spread or variability of the data
