April and Heather began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. April took a test in Science and earned a 74.4, and Heather took a test in English and earned a 69.7. Use the fact that all the students' test grades in the Science class had a mean of 71.3 and a standard deviation of 8.9, and all the students' test grades in English had a mean of 60.5 and a standard deviation of 8.5 to answer the following questions. a) Calculate the z-score for April's test grade. b) Calculate the z-score for Heather's test grade. c) Which person did relatively better? April Heather They did equally well.
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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