Population Variance ( measures spread )
Population Variance (σ^2) = Σ(x – µ)^2 / N
Population Variance: Variance is a statistical measure that quantifies the spread or dispersion of a set of data values. Population variance, specifically, refers to the variance of the entire population of interest. It is calculated by finding the average of the squared deviations of each value from the mean of the population, then taking the square root of that value.
The population variance is important because it helps us understand how much the values in a particular population vary from one another. If the variance is high, it means there is a lot of variability in the data, and if it is low, there is less variability. This information can be used to make decisions or draw conclusions about the population as a whole.
To calculate population variance, we use the following formula:
Population Variance (σ^2) = Σ(x – µ)^2 / N
Where:
– Σ: summation symbol, which means we add up all the values in the equation
– x: each individual value in the population
– µ: the population mean
– N: the total number of values in the population.
For example, let’s say we want to calculate the population variance of heights of all people living in a city. We measure the height of all people (the population), find the mean height (µ), then calculate the variance using the formula above. This will give us an idea of how much the heights in the population vary from one another.
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