You may want to calculate the z-scores of your raw data for many reasons. Whether you’re working with data related to stock metrics, medical trials, or exam scores, z-scores tell you where specific observations fit in the distribution of your dataset. Z-scores are useful in any field that relies on probability and statistics, such as finance, medicine, academic performance, or quantitative research in general. If the z-score is negative, your value is below the mean. Since this distance is measured using the population standard deviation, if the z-score is 0, your value is equal to the mean. Z-scores measure how far a specific value lies from the population mean. In the second example, you have the entire set of values, so you’ll have to calculate the mean and standard deviation before calculating the z-scores.In the first example, you have the mean and standard deviation for the population, and you need to calculate the z-score for three specific values.Now that you know how to calculate z-scores manually let’s see how easy it is to do it in Google Sheets. How to Calculate the Z-Score with Google Sheets? z-score3 = (x - μ) / σ = (70 - 71.73) / 15.83 = -3.08Īs you can see, the second score is closest to the mean, while the third is a full three standard deviations below the mean.To find the z-score for each test score, you’ll need to use the z-score formula, knowing that μ = 71.73 and σ = 15.83. The test scores that need to be standardized - converted to z-scores - are as follows: You know the average score (71.73) and the standard deviation (15.83). Imagine you’ve been given three test scores and some information about the test. In this section, you will learn how to calculate z-scores manually and using Google Sheets. There are three steps involved in calculating the z-score: find the population mean, find the population standard deviation, and apply the z-score formula. z-score = (x - μ) / σ How to Calculate the Z-Score? To get the z-score, subtract the population mean from the raw score and divide the result by the population standard deviation. There are three variables to consider when calculating a z-score: the raw score (x), the population mean (μ), and the population standard deviation (σ). The z-score’s unit of measure is the dataset’s standard deviation, and the sign indicates whether the value is above or below the mean.
Z-scores, which are sometimes referred to as standard scores, measure the distance between specific values - raw scores - and the mean of the dataset.
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