Single Sample Z Score Calculator

This tool calculates the z score of the mean of a single sample. It can be used to make a judgement about whether the sample differs significantly on some axis from the population from which it was originally drawn.

By default, this tool works on the assumption that you already know the mean value of your sample scores and the number of individuals in your sample. If you want the tool to calculate these for you from raw values, please select the checkbox below.

Note: To use this tool, you've got to know the mean of the population from which the sample is drawn (i.e., the population mean) and its variance (which is its standard deviation squared). There's no way around that!

Please input the population mean, population variance, sample mean and the number of individuals in the sample. You also need to select a significance level and whether your hypothesis is one or two-tailed. Hit the calculate button (below) when you're ready.

Population Mean (μ):
Population Variance (σ2):
Sample Mean (M):
Sample Size (n):

Significance Level:

One-tailed or two-tailed hypothesis?:

Z score not yet calculated. Z score will appear here.


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