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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.
Occasionally the percentile rank of a score is mistakenly defined as the percentage of scores lower than or equal to it [citation needed], but that would require a different computation, one with the 0.5 × F term deleted. Typically percentile ranks are only computed for scores in the distribution but, as the figure illustrates, percentile ...
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).
Suppose that in a particular geographic region, the mean and standard deviation of scores on a reading test are 100 points, and 12 points, respectively. Our interest is in the scores of 55 students in a particular school who received a mean score of 96.
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 ...
Since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal (known as a z-score) and then use the standard normal table to find probabilities. [2]
In the context of examinations, the raw data might be described as a raw score (after test scores). If a scientist sets up a computerized thermometer which records the temperature of a chemical mixture in a test tube every minute, the list of temperature readings for every minute, as printed out on a spreadsheet or viewed on a computer screen ...