National park services, a bureau of the US government responsible for park management, is interested in how the scores of their park rangers today are better or worse than in the past. The cognitive test that the forest rangers take as remained the same over the last five years. Below are the scores for each year, compute the mean, median, mode, range, and standard deviation for each year. Current Year 56, 45, 64, 75, 87, 81, 69, 81, 58, 92, 99, 95, 75, 92, 73, 83, 47, 69, 57, 74, 62, 74, 73, 100, 83 Five Years Ago 66, 78, 75, 79, 59, 74, 55, 89, 55, 79, 68, 27, 69, 95, 68, 90, 65, 79, 69, 79, 87, 86, 98, 81, 96
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.
Current Year
56, 45, 64, 75, 87, 81, 69, 81, 58, 92, 99, 95, 75, 92, 73, 83, 47, 69, 57, 74, 62, 74, 73, 100, 83
Five Years Ago
66, 78, 75, 79, 59, 74, 55, 89, 55, 79, 68, 27, 69, 95, 68, 90, 65, 79, 69, 79, 87, 86, 98, 81, 96
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