Calculating Z-Scores | A Statistical Measurement for Standardization and Comparison of Data Points

z Score

The z-score, also known as the standard score, is a statistical measurement that represents the number of standard deviations a given data point or value is from the mean of a data set

The z-score, also known as the standard score, is a statistical measurement that represents the number of standard deviations a given data point or value is from the mean of a data set. It is a way to standardize and compare values from different normal distributions.

To calculate the z-score, you subtract the mean of the data set from the specific data point, and then divide the result by the standard deviation. The formula for calculating the z-score is:

z = (x – μ) / σ

Where:
z = z-score
x = specific data point
μ = mean of the data set
σ = standard deviation of the data set

The resulting z-score can be positive or negative, indicating whether the data point is above or below the mean, respectively. A z-score of 0 means the data point is exactly at the mean of the distribution.

Z-scores are useful in statistical analysis as they allow for the comparison of data points from different distributions, regardless of the units or scales used in the original data. They also help in identifying outliers, as any data point with a z-score greater than 3 or less than -3 is often considered unusual or outside the normal range.

In addition, z-scores enable the calculation of percentiles, as they can be converted to percentile ranks. For example, a z-score of 1 corresponds to the 84th percentile, meaning the data point is greater than approximately 84% of the values in the distribution.

Overall, z-scores are a valuable tool in statistical analysis, allowing for standardization and comparison of data points across different distributions.

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