Suppose Ted is creating a football team in a video game that features many NFL players. He decides to identify players who are outliers in a few statistics he has chosen. Currently, he's looking at wide receivers. The game includes the top 100 receivers in 2012 by number of receptions. Ted, however, is more interested in receiving yards, and the table shows the five-number summary of the available players in the game (in yards): Minimum 1st quartile (Q1) Median 3rd quartile (Q3) Maximum 258.0 549.5 743.0 936.5 1964.0 The mean is 787.6 yds with a standard deviation of 311.3 yds. Ted first calculates the interquartile range (IQR). Next, to determine suspected outliers, he calculates Q1−1.5⋅???Q1−1.5⋅IQR and Q3+1.5⋅???Q3+1.5⋅IQR. Specify those results to at least one decimal place. Q1−1.5⋅???Q1−1.5⋅IQR = Q3+1.5⋅???Q3+1.5⋅IQR =
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.
Suppose Ted is creating a football team in a video game that features many NFL players. He decides to identify players who are outliers in a few statistics he has chosen.
Currently, he's looking at wide receivers. The game includes the top 100 receivers in 2012 by number of receptions. Ted, however, is more interested in receiving yards, and the table shows the five-number summary of the available players in the game (in yards):
| Minimum | 1st quartile (Q1) | Median | 3rd quartile (Q3) | Maximum |
|---|---|---|---|---|
| 258.0 | 549.5 | 743.0 | 936.5 | 1964.0 |
The mean is 787.6 yds with a standard deviation of 311.3 yds.
Ted first calculates the interquartile range (IQR). Next, to determine suspected outliers, he calculates Q1−1.5⋅???Q1−1.5⋅IQR and Q3+1.5⋅???Q3+1.5⋅IQR. Specify those results to at least one decimal place.
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