The following times were recorded by the quarter-mile and mile runners of a universitytrack team (times are in minutes).Quarter-Mile times: .92 .98 1.04 .90 .99Mile times: 4.52 4.35 4.60 4.70 4.50After viewing this sample of running times, one of the coaches commented that the quartermilers turned in the more consistent times. Use the standard deviation and the coefficientof variation to summarize the variability in the data. Does the use of the coefficient ofvaria tion indicate that the coach’s statement should be qualified?
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.
The following times were recorded by the quarter-mile and mile runners of a university
track team (times are in minutes).
Quarter-Mile times: .92 .98 1.04 .90 .99
Mile times: 4.52 4.35 4.60 4.70 4.50
After viewing this sample of running times, one of the coaches commented that the quartermilers turned in the more consistent times. Use the standard deviation and the coefficient
of variation to summarize the variability in the data. Does the use of the coefficient of
varia tion indicate that the coach’s statement should be qualified?
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