Statistics are widely used in Major League Baseball. Does a baseball player's batting average (AVG) determine their salary? The following is a chart of 25 baseball players' statistics from 2016. Let the explanatory variable x  = AVG and the response variable y  = Salary. Player RBI HR AVG Salary (in millions) Buster Posey 80 14 0.288 20.802 Mark Teixeira 44 15 0.204 23.125 Aaron Hill 38 10 0.262 12.000 Hunter Pence 57 13 0.289 18.500 Coco Crisp 55 13 0.231 11.000 Jacoby Ellsbury 56 9 0.263 21.143 Chris Davis 84 38 0.221 21.119 Jean Segura 64 20 0.320 2.600 Troy Tulowitzki 79 24 0.256 20.000 Justin Smoak 34 14 0.217 3.900 Leonys Martin 47 15 0.245 4.150 Hanley Ramirez 111 30 0.286 22.750 Adrian Beltre 104 32 0.300 18.000 Adrian Gonzalez 90 18 0.285 21.857 Adam Jones 83 29 0.265 16.000 Joe Mauer 49 11 0.261 23.000 Chris Iannetta 24 7 0.210 4.550 Curtis Granderson 59 30 0.237 16.000 Jason Heyward 49 7 0.230 21.667 Prince Fielder 44 8 0.212 18.000 Carlos Gonzalez 100 25 0.298 17.454 Jayson Werth 70 21 0.244 21.571 Matt Holliday 62 20 0.246 17.000 Joey Votto 97 29 0.326 20.000 Mike Trout 100 29 0.315 16.083 Create a scatter diagram and determine the type of linear correlation? A) weak negative linear correlation B) strong positive linear correlation C) strong negative linear correlation D) no linear correlation E) weak positive linear correlation

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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.