BenoguigoliB

2020-12-29

Regarding z-scores: a. How is a z-score obtained? b. What is the interpretation of a z-score? c. An observation has a z-score of 2.9. Roughly speaking, what is the relative standing of the observation?

The Z-score evaluates how closely a given value relates to the mean of a set of values. It provides the specific data point's standard deviation from the mean. The general formula $Z=\frac{\text{x – population mean}}{\text{population standard deviation}}$ b.

Case 1: If a data point has a Z-score of -3, this indicates that the data point is 3 standard deviations away from the mean.

Case 2: If a data point has a Z-score of 0, it means that the data point is 0 standard deviations away from the mean. The data point is therefore equal to the mean.

Case 3: If a data point has a Z-score of 3, this indicates that the data point is 3 standard deviations above the mean. c. Because over 95% of values in normal distributions fall within two standard deviations, the observation is relatively high.

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