객관식
In introductory statistics, which symbol is most commonly used to represent the (population) standard deviation?
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3. Describing Data Numerically
Standard Deviation
객관식
In introductory statistics, which formula should you use to compute the sample variance from data values , , ..., with sample mean ?
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Identify that the sample variance is a measure of how spread out the data values are around the sample mean. It is calculated by averaging the squared deviations from the mean, but with a correction in the denominator to account for sample size.
Recall the formula for the sample mean: \(\overline{x} = \frac{1}{n} \sum_{i=1}^n x_i\), where \(x_i\) are the data values and \(n\) is the sample size.
Calculate the squared deviations for each data point: \((x_i - \overline{x})^2\) for \(i = 1, 2, ..., n\).
Sum all the squared deviations: \(\sum_{i=1}^n (x_i - \overline{x})^2\).
Divide this sum by \(n - 1\) (not \(n\)) to get the sample variance: \(s^2 = \frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n - 1}\). This denominator adjustment is known as Bessel's correction and provides an unbiased estimate of the population variance.
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