- #1
Gerenuk
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Which of the generalized means (like http://en.wikipedia.org/wiki/Generalized_mean and more general) do you think is most suitable to approximate the median?
Generalized mean and median are statistical measures used to describe the central tendency of a set of data. The generalized mean is calculated by taking the nth root of the sum of the nth powers of each data value, where n is a positive integer. The generalized median is the middle value when the data is arranged in ascending or descending order.
The arithmetic mean is the sum of all data values divided by the number of values, while the arithmetic median is the middle value when the data is arranged in ascending or descending order. Generalized mean and median take into account the power of each data value, making them more sensitive to extreme values and providing a more accurate representation of the data's central tendency.
Generalized mean and median are useful when dealing with data that has a skewed distribution or contains extreme values. They are also commonly used in finance and economics to calculate average rates of return or income distributions.
To calculate the generalized mean, first raise each data value to the nth power, where n is a positive integer. Then, find the sum of these values and take the nth root of the sum. To calculate the generalized median, arrange the data in ascending or descending order and find the middle value. If there is an even number of values, take the average of the two middle values.
Yes, generalized mean and median can be used with any type of data that can be represented numerically. This includes both continuous and discrete data, as well as positive and negative values. However, it is important to note that for some types of data, such as count data or categorical data, other measures of central tendency may be more appropriate.