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The Common Admission Test (CAT), like virtually all large-scale exams, utilises multiple forms, or versions, of the test. Hence there are two types of scores involved: a raw score and a scaled score. The raw score is calculated for each section based on the number of questions one answered correctly, incorrectly, or left unattempted.
In statistics, a k-th percentile, also known as percentile score or centile, is a score below which a given percentage k of scores in its frequency distribution falls ("exclusive" definition) or a score at or below which a given percentage falls ("inclusive" definition); i.e. a score in the k-th percentile would be above approximately k% of all scores in its set.
The figure illustrates the percentile rank computation and shows how the 0.5 × F term in the formula ensures that the percentile rank reflects a percentage of scores less than the specified score. For example, for the 10 scores shown in the figure, 60% of them are below a score of 4 (five less than 4 and half of the two equal to 4) and 95% are ...
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.
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 the normal equivalent score is 99 if the percentile rank of the raw score is 99; the normal equivalent score is 50 if the percentile rank of the raw score is 50;
A confidence interval approach is also used, where after each item is administered, the algorithm determines the probability that the examinee's true-score is above or below the passing score. [ 16 ] [ 17 ] For example, the algorithm may continue until the 95% confidence interval for the true score no longer contains the passing score.
Changes include a new 130–170 scoring scale, the elimination of certain question types such as antonyms and analogies, the addition of an online calculator, and the elimination of the CAT format of question-by-question adjustment, in favor of a section by section adjustment.
In probability and statistics, the 97.5th percentile point of the standard normal distribution is a number commonly used for statistical calculations. The approximate value of this number is 1.96 , meaning that 95% of the area under a normal curve lies within approximately 1.96 standard deviations of the mean .