Understanding Z-Scores: How to Calculate and Interpret Standardized Scores in Statistics

Z-score formula

The Z-score formula is used to calculate the standard score, also known as the Z-value or Z-score, of a given data point in a distribution

The Z-score formula is used to calculate the standard score, also known as the Z-value or Z-score, of a given data point in a distribution. It tells you how many standard deviations a data point is away from the mean of the distribution.

The formula for calculating the Z-score is:

Z = (X – μ) / σ

Where:
Z is the Z-score,
X is the data point you want to find the Z-score for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.

To calculate the Z-score, you subtract the mean from the data point and then divide it by the standard deviation.

For example, let’s say you have a data point of 75 in a distribution with a mean of 60 and a standard deviation of 10. You can calculate the Z-score as follows:

Z = (75 – 60) / 10
Z = 15 / 10
Z = 1.5

So, the Z-score for the data point 75 in this distribution is 1.5. This means that the data point is 1.5 standard deviations above the mean.

Z-scores are a helpful tool in statistics as they allow you to compare data points from different distributions, determine outliers, and find the relative position of a data point within a distribution.

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