True position calculator
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Measures of Position
A measure of position is a method by which the position that a particular data value has within a given data set can be identified.
As with other types of measures, there is more than one approach to defining such a measure.
Standard Scores
The standard score (often called the z-score) of a particular data value gives the position of that data value by determining its distance from the mean, in units of standard deviation.
Therefore, the formula for the z-score when population data is involved is $z=\dfrac{x-\mu}{\sigma}$, and when sample data is involved is $z=\dfrac{x-\bar{x}}{s}$.
For example, suppose the grades on an economics exam averaged 78%, with a standard deviation of 5 percentage points.
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If Tom earned 69% on that exam, then his z-score was $z=\dfrac{69-78}{5} = \dfrac{-9}{5}=-1.8$. That is, he scored 1.8 standard deviations below the mean score.
To compute a standard score, only the mean and standard deviation are required.
However, since both of those quantities do depend on every value
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