How is the variance of a sample calculated?
Understand the Problem
The question is asking for the correct method to calculate the variance of a sample from the provided options. It requires knowledge of statistical formulas and concepts related to variance.
Answer
Sample variance is s^2 = (1/(n-1)) * Σ(x_i - x̄)^2.
The variance of a sample is calculated by finding the mean of the squared deviations from the sample mean. Specifically, the sample variance formula is s^2 = (1/(n-1)) * Σ(x_i - x̄)^2, where n is the sample size, x_i represents each value, and x̄ is the sample mean.
Answer for screen readers
The variance of a sample is calculated by finding the mean of the squared deviations from the sample mean. Specifically, the sample variance formula is s^2 = (1/(n-1)) * Σ(x_i - x̄)^2, where n is the sample size, x_i represents each value, and x̄ is the sample mean.
More Information
The sample variance is an important statistical measure of the dispersion within a sample data set. Unlike the population variance, it divides by n - 1 (where n is the sample size), which is known as Bessel's correction. This correction makes the variance an unbiased estimator of the population variance.
Tips
A common mistake is dividing by n instead of n-1. It's crucial to use n-1 to account for the bias in estimation for a sample.
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