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where z is the standard score or "z-score", i.e. z is how many standard deviations above the mean the raw score is (z is negative if the raw score is below the mean). The reason for the choice of the number 21.06 is to bring about the following result: If the scores are normally distributed (i.e. they follow the "bell-shaped curve") then
Comparison of the various grading methods in a normal distribution, including: standard deviations, cumulative percentages, percentile equivalents, z-scores, T-scores. In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured.
Numeric scores (or possibly scores on a sufficiently fine-grained ordinal scale) are assigned to the students. The absolute values are less relevant, provided that the order of the scores corresponds to the relative performance of each student within the course. These scores are converted to percentiles (or some other system of quantiles).
Like stanines, individual sten scores are demarcated by half standard deviations. Thus, a sten score of 5 includes all standard scores from -.5 to zero and is centered at -0.25 and a sten score of 4 includes all standard scores from -1.0 to -0.5 and is centered at -0.75. A sten score of 1 includes all standard scores below -2.0.
The multiple choice section is scored by computer, with a correct answer receiving 1 point, with omitted and incorrect answers not affecting the raw score. This total is multiplied by 1.2 to calculate the adjusted multiple-choice score. [26] The free response section is hand-graded by hundreds of AP teachers and professors each June. [27]
A standard score is a way of placing a raw score in context. It is often used to compare test results within and between groups, and especially with reference to a norm group. - dcljr 21:11, 9 Aug 2004 (UTC)
A scaled score is the result of some transformation(s) applied to the raw score, such as in relative grading. The purpose of scaled scores is to report scores for all examinees on a consistent scale. Suppose that a test has two forms, and one is more difficult than the other. It has been determined by equating that a score of 65% on form 1 is ...
In the case of normalization of scores in educational assessment, there may be an intention to align distributions to a normal distribution. A different approach to normalization of probability distributions is quantile normalization , where the quantiles of the different measures are brought into alignment.