## **Core Concept**
A z-score, also known as a standard score, indicates how many standard deviations an element is from the mean. It is a measure used in statistics to compare individual data points to the average value of a dataset, taking into account the variability of the dataset.

## **Why the Correct Answer is Right**
The formula for calculating a z-score is ( z = frac{(X - mu)}{sigma} ), where (X) is the value of the element, (mu) is the mean of the dataset, and (sigma) is the standard deviation. This formula shows that the z-score is directly related to the mean and standard deviation of a dataset. Therefore, option , which represents ( frac{(X - mu)}{sigma} ), is the correct answer because it accurately reflects the formula for a z-score.

## **Why Each Wrong Option is Incorrect**
- **Option A:** is incorrect because it does not accurately represent the formula for a z-score. This option seems to confuse the z-score formula with another statistical measure.
- **Option B:** is incorrect because, although it includes the mean ((mu)) and a value ((X)), it lacks the standard deviation ((sigma)), which is crucial for calculating a z-score.
- **Option D:** is incorrect because it incorrectly places the standard deviation in the denominator and does not accurately represent any standard statistical formula related to the z-score.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that a z-score of 0 means the data point is equal to the mean, a z-score greater than 0 indicates the data point is above the mean, and a z-score less than 0 indicates it is below the mean. About 68% of the data falls within one standard deviation (z-scores between -1 and 1) of the mean.

## **Correct Answer:** .