Calculating z-scores

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What is a z-score?

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A z-score is a statistical measurement that describes a value's relationship to the mean of a group of values. It indicates how many standard deviations an element is from the mean.

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How do you calculate a z-score?

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The formula for calculating a z-score is: z = (x - mean) / standard deviation, where x is the value, mean is the average of the dataset, and standard deviation measures the dispersion of the dataset.

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What does a positive z-score indicate?

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A positive z-score indicates that the value is above the mean of the dataset.

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What does a negative z-score indicate?

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A negative z-score indicates that the value is below the mean of the dataset.

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If the mean is 40 and the standard deviation is 1.4, what is the z-score for x = 42?

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z = (42 - 40) / 1.4 = 1.43.

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If the mean is 45 and the standard deviation is 2.1, what is the z-score for x = 50?

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z = (50 - 45) / 2.1 = 2.38.

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If the mean is 22.8 and the standard deviation is 7, what is the z-score for x = 20?

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z = (20 - 22.8) / 7 = -0.4.

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How do you find the mean of a dataset?

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To find the mean, sum all the values in the dataset and divide by the number of values.

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How do you find the standard deviation of a dataset?

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To find the standard deviation, calculate the square root of the variance, which is the average of the squared differences from the mean.

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What is the z-score for x = 14 in the dataset {15, 9, 27, 29, 37, 17, 30}?

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First, find the mean and standard deviation of the dataset, then use the z-score formula. The z-score is -1.02.