Calculation From Raw Score
The standard score of a raw score x is
where:
- μ is the mean of the population;
- σ is the standard deviation of the population.
The quantity z represents the distance between the raw score and the population mean in units of the standard deviation. z is negative when the raw score is below the mean, positive when above.
A key point is that calculating z requires the population mean and the population standard deviation, not the sample mean or sample deviation. It requires knowing the population parameters, not the statistics of a sample drawn from the population of interest. But knowing the true standard deviation of a population is often unrealistic except in cases such as standardized testing, where the entire population is measured. In cases where it is impossible to measure every member of a population, the standard deviation may be estimated using a random sample.
Read more about this topic: Standard Score
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—Henri-Frédéric Amiel (1821–1881)
“And we can get back to that raw state
Of feeling, so long deemed
Inconsequential and therefore appropriate to our later musings
About religion, about migrations. What is restored
Becomes stronger than the loss as it is remembered;
Is a new, separate life of its own.”
—John Ashbery (b. 1927)
“Whereas, before, our forefathers had no other books but the score and the tally, thou hast caused printing to be used, and, contrary to the King, his crown, and dignity, thou hast built a paper-mill.”
—William Shakespeare (1564–1616)