Raw scores on standardized tests are often transformed for easier comparison. A test of Math ability has a Mean of 153 and a Standard Deviation of 10 when given to 3rd-graders. While 6th-graders have a Mean of 164 and a Standard Deviation of 7 on the same test. Leslie is a 3rd-grade student who scores 159 on the test. Hollis is a 6th-grade student who scores 168 on the test. Calculate the z-score for each student. Who scored higher within their grade-level?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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