How To Report Z-Score Results

A Z-Score, also known as a standard score, is a statistical measurement that calculates the number of standard deviations that a given raw score is above or below the mean. Z-scores are calculated in the normal distribution, which is a symmetrical, bell-shaped theoretical distribution where the mean, median and mode coincide at its peak. This type of distribution explains how well a sample represents a population.

Step 1

Gather the data for the distribution. Graph the data on a bell-shaped curve, also called a standard normal curve. The mean, median and mode should all be at the center of the table under a bell-shaped curve. Use this data to calculate the Z-score. The formula for calculating a Z-score is Z= Y-Ybar/Sy. Ybar represents the mean of the population and is symbolized as a Y with a bar over it. Sy represents the standard deviation of the population.

Step 2

Use the standard normal table to see the value of the Z-score in proportion to the area between the mean and a given Z-score and the area beyond a given Z-score. The values on a standard normal table represent values under the standard normal curve.

Step 3

Report the Z-score results by identifying the population and data set the Z-score was computed for. A data set is a collection of data that represents variables and their values. In statistics, data sets come from sampling statistical populations and analyzing the data.

Step 4

Explain the type of analysis you used. Describe the data set of the raw scores that the Z-scores were computed for. The raw scores are the values collected in the data set. Display this data in a table of columns and rows with the names of the variables, the raw scores in one column, and the corresponding Z-scores in the other.

Step 5

Interpret your results. State the values of the raw scores and Z-scores. A positive Z-score indicates a score that is higher than the mean. A negative Z-score indicates a score that is less that the mean. The larger the Z-score, the greater difference there is between the score and the mean.