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Only 50 are scored; the other 10 (randomly scattered throughout the exam) are used for experimental purposes. The raw score is converted to a "scaled score" based on the measured difficulty of the version of the test taken; the scaled score is used to determine passing scores. Scaled scores range between 50 and 150, with a median very close to 100.
Percentile ranks are not on an equal-interval scale; that is, the difference between any two scores is not the same as between any other two scores whose difference in percentile ranks is the same. For example, 50 − 25 = 25 is not the same distance as 60 − 35 = 25 because of the bell-curve shape of the distribution. Some percentile ranks ...
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;
Age equivalent, grade equivalent, percentile marks and scaled scores are four of the normative scores of TOWRE - 2, however, the authors recommend to use percentile marks and scaled scores to interpret test results rather than age and grade equivalent.
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: the sample minimum (smallest observation) the lower quartile or first quartile; the median (the middle value) the upper quartile or third quartile; the sample maximum (largest observation)
In statistics, the 68–95–99.7 rule, also known as the empirical rule, and sometimes abbreviated 3sr, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: approximately 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.
One of the most common robust measures of scale is the interquartile range (IQR), the difference between the 75th percentile and the 25th percentile of a sample; this is the 25% trimmed range, an example of an L-estimator. Other trimmed ranges, such as the interdecile range (10% trimmed range) can also be used.
Scores on both forms can be converted to a scale so that these two equivalent scores have the same reported scores. For example, they could both be a score of 350 on a scale of 100 to 500. Two well-known tests in the United States that have scaled scores are the ACT and the SAT. The ACT's scale ranges from 0 to 36 and the SAT's from 200 to 800 ...