A z-score, also known as a standard score, is a statistical measurement that describes a value's position in relation to the mean of a group of values. It is measured in terms of standard deviations from the mean.

Here's why it matters:

**1. Understanding Relative Position:** A z-score tells you how many standard deviations an element is from the mean. For instance, a z-score of +2.0 indicates a value is two standard deviations from the mean. This allows you to understand the relative position of data points within a data set.

**2. Comparing Different Data Sets:** Z-scores are particularly useful when you want to compare data points from different sets, which may have distinct means and standard deviations. By converting different sets of data into z-scores, you can compare and analyze data more accurately.

**3. Identifying Outliers**: Z-scores are also useful for identifying outliers in a data set. Generally, a z-score less than -3 or greater than +3 is considered an outlier.

**4. Normal Distribution Assumption:** In a normal distribution, z-scores can help determine the probability of a score occurring within a given standard deviation. For instance, you can use the z-score to tell that approximately 95% of values in a normal distribution lie within 2 standard deviations of the mean.

**5. Standardization:** Z-scores are a way to standardize data, which makes data manipulation easier and more meaningful. It allows for the comparison of scores between different types of data.

In conclusion, z-scores are a powerful tool in statistics that allow for relative comparison of data points, identification of outliers, and easier manipulation and understanding of data.

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Check out our **YouTube tutorials** on z-scores in **R**, Python, and **Stata**.