For the five days from April 19-23, Sam counted the number of cups of caffeinated drinks he consumed (X) and the number of non-caffeinated drinks he consumed (Y). The following were the raw data for X and Y: Date X = # caffeinated drinks Y = # non-caffeinated drinks April 19 3 5 April 20 4 5 April 21 6 3 April 22 10 0 April 23 7 2 The mean and standard deviation for X (i.e., # of caffeinated drinks Sam drank) and the mean and standard deviation for Y (i.e., # of non-caffeinated drinks Sam drank) are
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.
For the five days from April 19-23, Sam counted the number of cups of caffeinated drinks he consumed (X) and the number of non-caffeinated drinks he consumed (Y). The following were the raw data for X and Y:
| Date | X = # caffeinated drinks | Y = # non-caffeinated drinks |
|---|---|---|
| April 19 | 3 | 5 |
| April 20 | 4 | 5 |
| April 21 | 6 | 3 |
| April 22 | 10 | 0 |
| April 23 | 7 | 2 |
| meanX = 6 | meanY = 3.6 |
|---|---|
| stdDevX = 2.45 | stdDevY = 1.9 |
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