Hi Srikanth,

Statistical moments give information about the location and characteristics of a given probability distribution. In particular central moments or moments referred to the mean of the distribution tell us whether the distribution is symmetrical or it is peaky when compared with the standard normal distribution.

Skewness is calculated from the 3rd central moment and it is a measure of the asymmetry of the distribution, there are other measures of skewness but by far the simplest and more widely used is the Pearson's moment coefficient of skewness, defined as the 3rd central moment divided by (standard deviation)**3.

Hope it helps,

Augusto

Third moment used for measuring skewness of a distribution.

In normal condition, 1st Central moment = mean, second= variance of that distribution.

Third and fourth Central moments are used for measuring skewness and kurtosis of the distribution respectively.

Points of correction: 1) The first central moment is not the mean but equal to zero. The mean is the first raw moment. 2) Skewness is not used to calculate the third central moment. The third central moment is used to calculate the skewness.

Generally, we have two form of moments which are raw and centered moments. The third moment of central tendency is a measure which use in calculating skewness. If we show 3rd moment and standard deviation by m3 and s then skewness measure can be calculated by m3/s^3 which use in assesing symmetry of a distribution.

Meanwhile, there are other forms of skewness measures which are based on percentiles and quartiles.

The question is confusing.

Central tendency is a characteristic of data while the third moment is a measure of the dispersion of data. Thus, "third moment of central tendency" is a meaningless term.