Now we can scroll up to our z-score reference above and find the intersection of 0.6 and 0.01, which should be .7291.
You calculate the z-score by first calculating the difference between your value and the mean, and then dividing that amount by the standard deviation of the set. While the Empirical Rule allows you to associate the first three standard deviations with the percentage of data that each SD includes, the z-score allows you to state (as accurately as you like), just how many SDs a given value is above or below the mean.Ĭonceptually, the z-score calculation is just what you might expect, given that you are calculating the number of SDs between a value and the mean. You can think of a z-score as the number of standard deviations there are between a given value and the mean of the set.
Z-scores are related to the Empirical Rule from the standpoint of being a method of evaluating how extreme a particular value is in a given set. It is worth noting, particularly for US students, that the instructor uses the notation x rather than µ for mean, and pronounces z as “zed.” If the population standard deviation is available and the sample size is greater than 30, t-distribution can be used with the population standard deviation instead of the sample standard deviation.The British video below is very clear and easy to follow. Summary: If the sample sizes are larger than 30, the z-distribution and the t-distributions are pretty much the same and either one can be used. The t-score is calculated using the formula: T-Score tells you how many standard deviations from the mean your result is.
If you are interested in T-test, you can do similar:
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