How to Calculate Z-Scores in a Bell Curve

Statistics bases many of its calculations on the assumption that collections of data are "normal." This means that a plot of the specific data values against the frequency with which each value occurs will have a single hill-shaped peak at the mean and will symmetrically trail off on either side. This distribution of values is also often called a bell curve because of its shape. Statisticians use a z-score to find the probability of a given value occurring within a data set. You can calculate a z-score for any given value if you first find the mean and the standard deviation of your data.

Things You'll Need

• Calculator

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Instructions

1. • 1

     Calculate the mean, or average, of your data set. This is found by summing all the values in the set, then dividing that sum by the quantity of values in the set. The mean is symbolized by the Greek letter "mu" or µ.

   • 2

     Calculate the standard deviation of your data set. This is a statistical measure of the degree of variation or spread among the values. Use the "σ" key on a scientific or statistical calculator to find this value from your data set. The symbol for standard deviation is the Greek letter sigma, or "σ."

   • 3

     Calculate the z-score for any value, x, by using the equation (x - µ)/σ.