The following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). Quarter-Mile times 0.91 0.97 1.03 0.90 0.98 Mile times 4.52 4.35 4.60 4.80 4.40 After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data. Compute the sample standard deviation (in min) for quarter-mile runners and one-mile runners. (Round your answers to four decimal places.) quarter-mile runners min one-mile runners min Compute the coefficient of variation for quarter-mile runners and one-mile runners. (Round your answers to one decimal place.) quarter-mile runners % one-mile runners %
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 0.91 0.97 1.03 0.90 0.98
Mile times 4.52 4.35 4.60 4.80 4.40
After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. Use the standard deviation and the coefficient of variation to summarize the variability in the data.
Compute the sample standard deviation (in min) for quarter-mile runners and one-mile runners. (Round your answers to four decimal places.)
quarter-mile runners
min
one-mile runners
min
Compute the coefficient of variation for quarter-mile runners and one-mile runners. (Round your answers to one decimal place.)
quarter-mile runners
%
one-mile runners
%
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