When you have multiple samples and want to describe the standard deviation of those sample means ( the standard error), you would use this z score formula: Z Score Formula: Standard Error of the Mean However, the steps for solving it are exactly the same. This is exactly the same formula as z = x – μ / σ, except that x̄ (the sample mean) is used instead of μ (the population mean) and s (the sample standard deviation) is used instead of σ (the population standard deviation). You may also see the z score formula shown to the left. In this example, your score is 1.6 standard deviations above the mean. The z score tells you how many standard deviations from the mean your score is. Assuming a normal distribution, your z score would be: The test has a mean (μ) of 150 and a standard deviation (σ) of 25. The basic z score formula for a sample is:įor example, let’s say you have a test score of 190. Z Score Formulas The Z Score Formula: One Sample A z-score can tell you where that person’s weight is compared to the average population’s mean weight.īack to Top 2. For example, knowing that someone’s weight is 150 pounds might be good information, but if you want to compare it to the “ average” person’s weight, looking at a vast table of data can be overwhelming (especially if some weights are recorded in kilograms). Results from tests or surveys have thousands of possible results and units those results can often seem meaningless. Z-scores are a way to compare results to a “normal” population. In order to use a z-score, you need to know the mean μ and also the population standard deviation σ. Z-scores range from -3 standard deviations (which would fall to the far left of the normal distribution curve) up to +3 standard deviations (which would fall to the far right of the normal distribution curve). But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.Ī z-score can be placed on a normal distribution curve. Simply put, a z-score (also called a standard score) gives you an idea of how far from the mean a data point is.
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