Bit More About z-Scores

The z-score indicates the distance an individual score is from the mean of a distribution. If a score is at the mean, it has a z-score of 0. Scores above the mean are positive and scores that are located below the mean are negative.

In practical terms, z-scores range from -3 to +3. A z of -3 indicates that the raw score is 3 standard deviations below the mean (at the extreme left end of the distribution). A z of 3 indicates that the raw score is at the extreme right end of the distribution.

Since z-scores are expressed in units of standard deviation, they are independent of the variable being measured. A z-score of -1.5 is one and a half standard deviations below the mean, regardless If z = .5, the score is located at one half standard deviation above the mean.

Composed of two parts, the z-score has both magnitude and sign. The magnitude can be interpreted as the number of standard deviations the raw score is away from the mean. The sign indicates whether the score is above the mean (+) or below the mean (-). To calculate the z-score, subtract the mean from the raw score and divide that answer by the standard deviation of the distribution. In formal terms, the formula is

Using this formula, we can find z for any raw score, assuming we know the mean and standard deviation of the distribution. What is the z-score for a raw score of 110, a mean of 100 and a standard deviation of 10? First, we find the difference between the score and the mean, which in this case would be 110-100 = 10. The result is divided by the standard deviation (10 divided by 10 = 1). With a z score of 1, we know that the raw score of 110 is one standard deviation above the mean for this distribution being studied.

Z-scores can be used to find an individual, standardize a distribution or set a cutoff. A z-score indicates a score’s distance from a mean, expressed in standard deviations. If a score is at the mean, z = 0. One standard deviation above the mean is indicated by z = 1. And one standard deviation below the mean is expressed as z = -1.

NOW YOU CHOOSE:
    Day 4: z-Score
    A Bit More About z-Scores
    Even More About z-Scores
    How To Calculate z-Scores
    Practice Problems
    Basic Facts About z-Scores
    Vocabulary
    Formulas For z-Scores
    Quiz 4
    Summary