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.
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.
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.
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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.
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.
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.