Refer to the variance formula page to see the algebra involved in re-arranging the formula.įind the variance of the following weights (lbs) obtained from a sample of students: 127, 134, 155, 171, and 202.Ģ.
Where s 2 is the variance of the sample, x i is the i th element in the set, x is the sample mean, and n is the sample size.Īnother form of the sample variance formula that can be computationally simpler (when calculating variance by hand) is: The formula for sample variance is similar to that for a population with some adjustments to account for the differences in data types: Refer to the variance formula page to see the algebra involved in re-arranging the formula. Where σ 2 is the variance of the population, x i is the i th element in the set, μ is the population mean, and N is the population size.Īnother form of the population variance formula that can be computationally simpler (when calculating variance by hand) is: Variance is commonly denoted as σ 2 or s 2 depending on whether it is a population or sample variance, respectively. Because it can be impractical or even impossible to collect data for an entire population, samples of a population are often gathered then used to make generalizations or inferences about the population as a whole. A statistical population is any complete group of observations or objects from which a sample is taken, while a sample comprises some subset of a population. The formula for variance changes depending on whether the variance is being calculated for a population or a sample. Variance is used throughout statistics in areas such as descriptive statistics, inferential statistics, hypothesis testing, and more.
A low variance tells us the opposite, that the collected data is generally similar, and does not deviate much from the mean. A high variance tells us that the collected data has higher variability, and the data is generally further from the mean. It is a statistical measurement of variability that indicates how far a set of numbers varies from the mean. Variance is the average of the squared differences of a random variable from its mean. Home / probability and statistics / descriptive statistics / variance Variance
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