measures of central tendencies mean, types of mean and their formula
Mean
Arithmetic mean
Arithmetic mean of a set of realisations of a variable is defined as their sum
divided by the number of observations. Depending on whether the data are grouped
or ungrouped arithmetic mean may be of two types. First, simple arithmetic
mean for ungrouped data and second, weighted arithmetic mean for grouped
(frequency type) data. If the realizations of the variable x are x1, x2…xn than,
Simple Arithmetic Mean ( x ) = (x1 + x2 +……. + xn) / n
Σ is the summation operator which sums over different values
taken by a variable. If the variable x takes the values x1, x2…xn with
frequencies f1, f2…fn then
Weighted arithmetic mean
_ _
Given two groups of observations, n 1 and n 2 , and x 1 and x 2 being the number
of observations and arithmetic mean of two groups respectively, we can
calculate the composite mean using the following formula:
_ _ _
Composite Mean ( x ) = (n 1 . x 1 + n 2 . x 2 ) / n 1 + n 2
Geometric mean
Geometric mean of a set of observations is nth root of their product, where n is the number of observation. In case of non frequency type data, simple geometric mean
and
in case of frequency type data weighted geometric mean
Harmonic mean
It is the reciprocal of the arithmetic mean and computed with the reciprocal of
the observations.
Arithmetic mean
Arithmetic mean of a set of realisations of a variable is defined as their sum
divided by the number of observations. Depending on whether the data are grouped
or ungrouped arithmetic mean may be of two types. First, simple arithmetic
mean for ungrouped data and second, weighted arithmetic mean for grouped
(frequency type) data. If the realizations of the variable x are x1, x2…xn than,
Simple Arithmetic Mean ( x ) = (x1 + x2 +……. + xn) / n
Σ is the summation operator which sums over different values
taken by a variable. If the variable x takes the values x1, x2…xn with
frequencies f1, f2…fn then
Weighted arithmetic mean
_ _
Given two groups of observations, n 1 and n 2 , and x 1 and x 2 being the number
of observations and arithmetic mean of two groups respectively, we can
calculate the composite mean using the following formula:
_ _ _
Composite Mean ( x ) = (n 1 . x 1 + n 2 . x 2 ) / n 1 + n 2
Geometric mean
Geometric mean of a set of observations is nth root of their product, where n is the number of observation. In case of non frequency type data, simple geometric mean
and
in case of frequency type data weighted geometric mean
Harmonic mean
It is the reciprocal of the arithmetic mean and computed with the reciprocal of
the observations.
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