We can also calculate the z-score for a sample of data. The z-score formula is given as: z = (x – μ)⁄ σ Where z is the z-score, x is the raw score, μ is the population mean, and σ is the population standard deviation. If the raw score is lesser than the mean, the z-score will be negative. If the raw score (the observed data point) is greater than the mean (the average of all data points), the z-score will be positive. The further away a value is from the mean, the higher the absolute value of the z-score will be for that value.įor example, the value 3 is further away from the mean compared to 4, which explains why 3 had a z-score with a larger absolute value.In statistics, the z-score (also called the standard score) is the number of standard deviations a raw score is from the mean. This means that the value “4” is 1.08 standard deviations below the mean. The next value in our dataset, 4, had a z-score of (4-10) / 5.558 = -1.08. This means that the value “3” is 1.259 standard deviations below the mean. So, the first value in our dataset was 3, which had a z-score of (3-10) / 5.558 = -1.259. In our example, we found that the mean was 10 and the standard deviation was 5.558. A z-score of zero indicates that a particular value is equal to the mean.A negative z-score indicates that a particular value is less than the mean.A positive z-score indicates that a particular value is greater than the mean.A z-score can be positive, negative, or equal to zero: Recall that a z-score simply tells us how many standard deviations away a value is from the mean. Note: To enter “L1” in the formula, press 2nd and then press 1. The z-score of every individual value will automatically appear in column L2: Highlight L2 and type in the formula ( L1-10) / 5.558 and then press Enter. Next, we will calculate the z-score for every individual value in the dataset. Step 3: Use a formula to calculate every z-score. We will use these two values in the next step to calculate z-scores. We can see that the mean of the dataset is x = 10 and the standard deviation is s x = 5.558. Press Stat and then scroll over to CALC. Highlight 1-Var Stats and press Enter.įor List, make sure L1 is chosen since this is the column we entered our data in. Next, we will find the mean and the standard deviation of the dataset. Step 2: Find the mean and standard deviation of the data values. In this case, we can perform the following steps:įirst, we will input the data values. Suppose instead that we have a list of data values and that we would like to calculate the z-score for every value in the list. How to Calculate the Z-Score of Several Values In other words, the value 14 lies 1.4286 standard deviations above the mean. This tells us that an individual value of 14 has a z-score of 1.4286. To calculate the z-score in a TI-84 calculator, we would simply type in the following formula: Suppose a distribution is normally distributed with a mean of 12 and a standard deviation of 1.4 and we wish to calculate the z-score of an individual value x = 14. How to Calculate the Z-Score of a Single Value This tutorial explains how to calculate z-scores on a TI-84 calculator. The z-score of a given value is calculated as: A z-score tells us how many standard deviations away a given value is from the mean.
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