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Alex's z score of 1.6 means her frequency of anxiety symptoms are 1.6 standard deviations more than the mean of all patients.
Z-score is defined as the relationship between a particular value or data to the mean of all the data present in a normal distribution. When the z-score is zero that means the data is equal to the mean.
where x=raw data,
=mean and
= standard deviation
Standard Deviation is a measure of how dispersed a data set is around its mean or central value. Numerically Standard deviation is defined as the square root of the variance of the distribution.
- Lower standard deviation means the data is clustered together
- A higher standard deviation means that the data is spread out over a larger area.
In the given problem as the z-score of Alex is given as 1.6, we can infer that the frequency of anxiety symptoms for Alex is 1.6 standard deviations more than the mean data.
Therefore from the above formula
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