How To Calculate Standardized Scores (Z-Scores) In Data Distributions

Find and interpret the standardized score (z-score) of an individual value in a distribution of data.

z-score = (value – mean) / standard deviation. If the z-score is x, the value is x standard deviations above/below the mean.

To find the standardized score (z-score) of an individual value in a distribution of data, you need to follow these steps:

Step 1: Find the mean (μ) and standard deviation (σ) of the distribution.

Step 2: Subtract the mean from the individual value of interest (X) and divide the result by the standard deviation. This calculation is expressed as: z = (X – μ) / σ

Step 3: Interpret the z-score. A z-score represents the number of standard deviations an individual value falls away from the mean. If the z-score is positive, it means that the individual value is above the mean, and if it is negative, it means the value is below the mean. Additionally, the farther the absolute value of the z-score is away from zero, the farther away the individual value is from the mean.

For example, let’s say we have a distribution of test scores with a mean of 75 and standard deviation of 10, and we want to find the z-score of a test score of 85.

Step 1: μ = 75, σ = 10

Step 2: z = (X – μ) / σ = (85 – 75) / 10 = 1

Step 3: The z-score is 1, which means the test score of 85 is one standard deviation above the mean of 75.

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