Data for a sample of 55 members of the baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), shortstop (S), left field (L), center field (C), and right field (R). L P C H 2 P R 1 S S 1 L P R P P P P R C S L R P C C P P R P 2 3 P H L P 1 C P P P S 1 L R R 1 2 H S 3 H 2 L P (a) Construct frequency and relative frequency distributions to summarize the data. (Round the relative frequencies to three decimal places.) Position Frequency Relative Frequency Pitcher Catcher 1st Base 2nd Base 3rd Base Shortstop Left Field Center Field Right Field Total (b) What position provides the most Hall of Famers? PitcherCatcher 1st Base2nd Base3rd BaseShortstopLeft FieldCenter FieldRight Field (c) What position provides the fewest Hall of Famers? PitcherCatcher 1st Base2nd Base3rd BaseShortstopLeft FieldCenter FieldRight Field (d) What outfield position (L, C, or R) provides the most Hall of Famers? Left FieldCenter Field Right Field (e) Compare infielders (1, 2, 3, and S) to outfielders (L, C, and R). There are more infielders than outfielders.There is the same number of infielders and outfielders. There are more outfielders than infielders.
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.
L | P | C | H | 2 | P | R | 1 | S | S | 1 |
L | P | R | P | P | P | P | R | C | S | L |
R | P | C | C | P | P | R | P | 2 | 3 | P |
H | L | P | 1 | C | P | P | P | S | 1 | L |
R | R | 1 | 2 | H | S | 3 | H | 2 | L | P |
Position | Frequency | Relative Frequency |
---|---|---|
Pitcher | ||
Catcher | ||
1st Base | ||
2nd Base | ||
3rd Base | ||
Shortstop | ||
Left Field | ||
Center Field | ||
Right Field | ||
Total |
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