merits and demerits of average??

Question

mathematics....arithmetic mean, geometric mean,harmonic mean, median, mode and their merits and demerits...

Answer 1

arithmetic mean: sum of all numbers divided by n
geometric mean: nth root of the product of the numbers.
harmonic mean: reciprocal of the arithmetic mean of the reciprocals.

median: the 50th percentile. arranged from lowest to highest, this is the middle value. If there are even entries get the average of the two middle values.

mode: the most repeated frequency, this need not be unique.

AM = (x1 + x2 + ... + xn)/n
GM = (x1*x2*...*xn)^(1/n)
HM = n/{1/x1 + 1/x2 + ... + 1/xn}
HM ≤ GM ≤ AM

these values are most often termed as measures of central tendency.

d:

Answer 2

arithmetic mean is simply (x1+x2+x3+ .... +xn)/n

geometric mean is n/(x1*x2*x3*x4 ..... *xn)^1/n

Harmonic mean is n/(1/x1+1/x2+1/x3 +.. ...1/xn)

median is the midlle number after the set of numbers is arranged in ascending or descending order. There are as many numbers below the median as there are above it.

The mode is the number in a set that occurs most frequently. A set of numbers may have several modes .

In general, it depends what your goals are when you choose which method to use. Each method can give inaccurate results depending on the data.

The arithmetic mean is useful if the data is random. But if the data cosists of 99 numbers all = 10 and one numbe = 1,000,000, the mean would give an inaccurate picture. The mode would be much more reliable.

The geometric mean is best when products are ivoved such as yearly % gains. If the gains for three years were 10%, 50% and 25%. the geometric mean provides the bes number to represent the average % gain over the three years. Mode and arithmetic mean would fail miserably.

The harmonic mean is useful in when fiding the average resistnce of n resistors in parallel. There are many other examples where the harmonic mean is the only way to go.

Answer 3

You are getting into mathematical metaphysics if you want to attach attibutes to these terms. If they weren't useful in one way or another, they wouldn't have been defined and kept around. In terms of theory, means are most conceptually important terms, based on the type of data being treated.

Answer 4

These different averages are not appropriate if negatives or zeros are included. In that case we need to use variance and standard deviation

Answer 5

do you mean main-streaming?