How is a z-score calculated?

The correct method for calculating a z-score is by subtracting the mean from the data point and then dividing that result by the standard deviation. This calculation transforms individual data points into a standardized score that indicates how many standard deviations away a data point is from the mean of the dataset.

The formula, which captures this process, is expressed as:

[ z = \frac{(X - \mu)}{\sigma} ]

where ( X ) is the data point, ( \mu ) is the mean, and ( \sigma ) is the standard deviation. This standardization allows for comparison across different datasets or distributions, as it normalizes the data in relation to its own distribution.

Using this method provides valuable information regarding the position of the specific data point within the overall distribution. A positive z-score indicates that the data point is above the mean, while a negative z-score indicates it is below the mean. This interpretation is essential for various statistical applications, such as assessing probabilities in a normal distribution.

Other methods listed do not provide the right approach for calculating a z-score. For instance, simply adding the mean to the data point does not yield standardized data, dividing the standard deviation by the data point does not relate to the mean of