Population Standard Deviation ( measures spread )
σ = √(Σ(x – μ)²/N)
Population standard deviation is a measure of spread that quantifies the amount of variability or dispersion in a population. It is calculated as the square root of the average squared differences of the values from the population mean. The equation for population standard deviation is as follows:
σ = √(Σ(x – μ)²/N)
Where σ represents the population standard deviation, Σ is the sum of, x is the value of an individual observation, μ is the population mean, and N is the total number of observations in the population.
Population standard deviation is useful in a variety of statistical analyses, including hypothesis testing, confidence interval estimation, and regression analysis. It provides valuable information about the variability and distribution of data in a population, which allows researchers to draw more accurate conclusions from their analyses.
In practice, population standard deviation is often estimated from sample standard deviation since it is usually impossible to measure the variance or standard deviation of an entire population.
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