Assume this is a randomly selected list of the total points scored in twenty-four Super Bowls: 36 37 37 39 39 41 43 44 44 47 50 53 54 55 56 56 57 59 61 61 65 69 69 75 a.) Find the four “measures of center” and the standard deviation. b.) Give the values of the 5-number summary. c.) Are there any scores that would be considered “unusually” high or low? Why or why not? d.) Based on the definition involving the interquartile range, are unusual values in part c, if any exists, considered to be outliers? Why or why not?
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.
5.) Assume this is a randomly selected list of the total points scored in twenty-four Super Bowls:
36 37 37 39 39 41 43 44 44 47 50 53 54 55 56 56 57 59 61 61 65 69 69 75
a.) Find the four “measures of center” and the standard deviation.
b.) Give the values of the 5-number summary.
c.) Are there any scores that would be considered “unusually” high or low? Why or why not?
d.) Based on the definition involving the
exists, considered to be outliers? Why or why not?
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