Would give the highest “average”? why? Would give the lowest “average”? why? Would be the most representative “average”? why?
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.
- Suppose a neighborhood has few expensive homes and many low value homes. Which measure of
central tendency
- Would give the highest “average”? why?
- Would give the lowest “average”? why?
- Would be the most representative “average”? why?
Expert Answer
From the given information,
Distribution of value of homes is positively skewed and for positively skewed distribution,
a. As Mode < Median < Mean, Hence Mean will give highest "average".
b. As Mode < Median < Mean, Hence Median will give lowest "average".
c. As distribution is positively skewed, Median is the most representative"average".
Does not in question b mode is the lowest average?
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