![]() In a nutshell, z-scores give us an idea of how individual values compare to the mean. Specifically, an exam score of 87 is 0.75 standard deviations below the mean. Since this value is negative, it tells us that an exam score of 87 is actually below the average exam score for the population. If the exam scores for the whole population are normally distributed with a mean of 90 and a standard deviation of 4, we would calculate the z-score for 87 to be: Z-scores are useful because they give us an idea of how an individual value compares to the rest of a distribution.įor example, is an exam score of 87 good? Well, that depends on the mean and standard deviation of all exam scores. This tells us that an exam score of 80 is exactly equal to the mean. The individual value we’re interested in is X = 80.Question 3: Find the z-score for an exam score of 80. This tells us that an exam score of 75 lies 1.25 standard deviations below the mean. The individual value we’re interested in is X = 75.Question 2: Find the z-score for an exam score of 75. This tells us that an exam score of 87 lies 1.75 standard deviations above the mean. Just enter your raw score, population mean and standard deviation. Thus, z = (X – μ) / σ = (87 – 80) /4 = 1.75. This simple calculator allows you to calculate a standardized z-score for any raw value of X.The individual value we’re interested in is X = 87.We can use the following steps to calculate the z-score: Question 1: Find the z-score for an exam score of 87. Suppose the scores for a certain exam are normally distributed with a mean of 80 and a standard deviation of 4. Example: Calculate and Interpret Z-Scores The following example shows how to calculate and interpret z-scores. The larger the absolute value of the z-score, the further away an individual value lies from the mean. Note: If you already know the value of z, and want to calculate p, this calculator will do the job. Just enter your raw score, population mean and standard deviation, and hit 'Calculate Z'. A z-score of 0: The individual value is equal to the mean. This simple calculator allows you to calculate a standardized z -score for any raw value of X.Negative z-score: The individual value is less than the mean.Positive z-score: The individual value is greater than the mean.We use the following formula to calculate a z-score:Ī z-score for an individual value can be interpreted as follows: If you're interested in using the z statistic for hypothesis testing, then we have a couple of other calculators that might help you.In statistics, a z-score tells us how many standard deviations away a given value lies from the mean. Please enter the value of p above, and then press "Calculate Z from P". Just enter your p-value, which must be between 0 and 1, and then hit the button below. This second calculator allows you to calculate the z-score for any given cummulative probability level (simply put, for any given value of p). Please enter your values above, and then hit the calculate button. ![]() Just enter your raw score, population mean and standard deviation, and hit "Calculate Z". This simple calculator allows you to calculate a standardized z-score for any raw value of X.
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