Without computing anything, determine how the means, medians, and standard deviations of the following data sets compare. Explain your reasoning. a) i) ii) 3,5,5,5,8,11,11,11,13 3,5,5,5,8,11,11,11,20 i) ii) b) -20,0,0,0,15,25,30,30 -40,0,0,0,15,25,30,30 c) i) 0,2,4,6,8,10 ii) 20,22,24,26,28,30
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.
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From the given information,
The comparison can be understood as below:
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