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You can find the z-score of a data point using a formula that compares the point to the average (mean) and variability (standard deviation) of the data set.

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Here's what you need to know:


The z-score formula is:

z = (x - μ) / σ

  • x is the value of your data point
  • μ (mu) is the population mean (average) of the data set
  • σ (sigma) is the population standard deviation of the data set


The z-score tells you how many standard deviations a specific point is away from the mean.

  • A positive z-score means the point is above the mean by that many standard deviations.
  • A negative z-score means the point is below the mean by that many standard deviations.

Finding the Mean and Standard Deviation:

  • You might already be given the mean and standard deviation of your data set.
  • If not, you'll need to calculate them yourself. There are formulas for both, but you can also use spreadsheet functions like STDEV.P for standard deviation and AVERAGE for mean in many software programs.

Online Calculators:

If you just need to calculate a z-score for a single data point, you can find online z-score calculators that will do the work for you.

Here are some resources that you might find helpful:

*の説明 (の説明 =の説明 [explanation in Japanese]) on z-scores: https://www.statisticshowto.com/probability-and-statistics/z-score/

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