Standard Deviation
the spread of scores around the mean
Standard deviation (SD) is a statistical measure used to quantify the amount of variability or dispersion in a set of data. It is a measure of how spread out the data is from the mean or average value. In simple terms, the standard deviation is the square root of the variance of a set of data.
The formula for calculating the standard deviation is as follows:
SD = √ [(Σ(xi – μ)²) / N]
where xi represents each data point, μ represents the mean of the data, and N represents the total number of data points.
The standard deviation is commonly used in various fields, including finance, science, and psychology. It is particularly useful in finance, where it is used to measure the volatility of a stock or portfolio. In science, it is used to analyze the reliability of data sets, and in psychology, it is used to analyze the variability of responses in research studies.
A low standard deviation indicates that the data is clustered closely around the mean, while a high standard deviation indicates that the data is more spread out from the mean. In general, the standard deviation is a useful tool for quantifying the variability of a set of data and can provide insights into the nature of the data.
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