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The Z-score formula is shown below. Z minus s c o r e equals begin fraction V a l u e minus M e a
The Z-score formula is shown below. Z minus s c o r e equals begin fraction V a l u e minus M e a n over S t a n d a r d D e v i a t i o n end fraction Every data value in a distribution has a Z-score. Z-scores can be negative, positive, or zero. When a Z-score is less than or equal to 2, or greater than or equal to 2, we say that the corresponding data value is unusual, since the data value is relatively far from the mean. In fact, only 5% of data values in a bell-shaped distribution will have a Z-score less than or equal to -2, or greater than or equal to 2. For example, consider the dataset from Problem Situation 2 and assume that the mean is 40 years and the standard deviation is 5 years. Next, consider a county with the median age of 55 years: One way to compare this county to the mean is by saying that the median age of 55 years is 15 years higher than the mean Another way to do it is by saying that the median age of
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