A set of exam scores are reported as X values and z-scores. On this exam a score of X = 72 corresponds to a z-score = +1.00 and a score of X = 52 corresponds to a z-score = -1.00. What are the values for the mean and standard deviation for this exam? Sketch a distribution and on it locate the mean, the standard deviation, and the two z-score positions.
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.
- A set of exam scores are reported as X values and z-scores. On this exam a score of X = 72 corresponds to a z-score = +1.00 and a score of X = 52 corresponds to a z-score = -1.00. What are the values for the
mean and standard deviation for this exam? Sketch a distribution and on it locate the mean, the standard deviation, and the two z-score positions.
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