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Concept

-Score

The score, also known as the value, represents the number of standard deviations that a given value is from the mean of a data set. The following formula can be used to convert any value into its corresponding score.

Here, represents the mean and the standard deviation of the distribution. The value corresponding to a sample mean is called a statistic and is calculated using a similar formula.

In this formula, is the standard deviation of the sample, is the sample size, and is the population mean.

Example

Consider a distribution with mean and standard deviation The score corresponding to is computed as follows.
Consequently, is standard deviations to the left of the mean. The scores can be used to standardize a normal distribution. Then, for a random value of a standard normal distribution, the Standard Normal Table can be used to determine the corresponding area under the curve.