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What on earth is aZ-score? While it might seem strange, it’s straightforward to understand. The Z-score is the standard score. The standard score is the number of standard deviations that a data point is above the mean. AZ-Score calculatorwill help you work out the value. Below, you can also learn how to calculate and use theZ-scoreandZ-score table.

TheZ-scoredefines the distance between a data point and a mean score. You use it to describe normal distribution. You would also explain it in standard deviation (SD) terms. Many people call it a Z-score, but you can also call it the standardized score, standard, z-value, or average score. You need to identify theSDand mean of a data set before you find a Z-score. The mean (μ) is the sum of values in a data set. You then divide them by the number of data points. The equation looks like this:μ = ∑x / nAnd you find SD according to this expression:σ = √ [∑ (x - μ) ² / n]x= raw valuen= number of data points Apply the following formula to find the Z-score:z = (x - μ) / σ

We’ll posit that you are playing darts with four friends. Your scores are 49, 56, 60, and 100. What is the Z-score of the friend who scored 60? 1. Find the mean of all the results. You can use an average calculator, or use the formula below.μ = (49 + 56 + 60 + 100) / 4 = 66.252. Calculate the values of (x - μ) ² for each dart score.(49 – 66.25) ² = 297.56 (56 – 66.25) ² = 105.062 (60 – 66.25) ² = 39.063 (100 – 66.25) ² = 1,139.0633. Calculate the standard deviation.√ [(297.56 + 105.062 + 39.063 + 1,139.063) / 4] = √ (1580.748 / 4) = 19.884. Input the results.z = (60 – 66.25) / 19.88 = 0.315. Get your answer. With that formula, you worked out the Z-score of 60. The Z-score calculator can also help you find your SD or mean, once you know your Z-score.

AZ-score tablelets you find the area of a Z-score in theSDgraph. The first column would have Z- values. In the first row, identify the number with the same second decimal place as your Z-score. Previously,we found the Z-score for 60. It was 0.31. You would have to locate 0.3 in the first column and 0.01 in the first row. The area in theSDgraph, left of the Z-score, offers a value. The area = 1. With this information, you can determine the probability of scoring less than 60 in darts.

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