# 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?

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?
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a. Z-score: The Z-score measures a particular value’s relationship to the mean in a group of values. It gives the number of standard deviation from the mean for the particular data point. The general formula to obtain Z-score is, $Z=\frac{\text{x – population mean}}{\text{population standard deviation}}$ b. Consider the following cases to interpret Z-scores:

Case1: If a Z-score of −3 is obtained for a data point, then it can be interpreted that the data point is 3 standard deviations below the mean.

Case2: If a Z-score of 0 is obtained for a data point, then it can be interpreted that the data point is 0 standard deviations from the mean. That is, the data point is equal to the mean.

Case3: If a Z-score of 3 is obtained for a data point, then it can be interpreted that the data point is 3 standard deviations above the mean. c. The observation is very high because for normal distributions, about 95% of values are within two standard deviations.