The mean defined in the text is sometimes called the arithmetic mean to distinguish it from other possible means. For example, a different mean, called the geometric mean (G.M.), is used in business and economics for finding average rates of change, average rates of growth, or average ratios. This mean is defined to be the nth root of the product of the numbers. For example, the geometric mean of 4, 5, and 6 is G.M. = (4 - 5-6)1/3 20 4.9- (a) Find the arithmetic and geometric means for the numbers 2, 4, 6, 7, 7, 8, and 10. (Round your answers tone decimal place.) arithmetic mean 6.3 geometric mean 7.9 (b) The growth rates for three cities are 1.5%, 2.1%, and 0.9%. Compare the arithmetic and geometric means. (Round your answers to two decimal places.) arithmetic mean 1.50 1.41 geometric mean
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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