Mean deviation and standard deviation are two measures of dispersion that are used to describe the variability of a dataset. Mean deviation is the average distance of each observation from the mean of the dataset, while standard deviation is the square root of the average squared distance of each observation from the mean.

Moderately Non-Symmetrical Distribution
A moderately non-symmetrical distribution is a type of distribution where the data is skewed but not to a great extent. It means that the data is not evenly distributed around the mean, but there are not too many extreme values that pull the mean away from the center.

Mean Deviation and Standard Deviation
As mentioned earlier, mean deviation is the average distance of each observation from the mean, while standard deviation is the square root of the average squared distance of each observation from the mean. The formula for mean deviation is:

Mean Deviation = Σ|Xi - X̄| / n

The formula for standard deviation is:

Standard Deviation = √(Σ(Xi - X̄)² / (n - 1))

Where Xi is the ith observation, X̄ is the mean of the dataset, and n is the number of observations.

Relation between Mean Deviation and Standard Deviation
It is a well-known fact that mean deviation is always less than or equal to standard deviation. This is because mean deviation is calculated by taking the absolute value of the deviations, while standard deviation is calculated by squaring the deviations.

4/5 of Standard Deviation
The statement "For a moderately non-symmetrical distribution, Mean deviation = 4/5 of standard deviation" is false. There is no fixed relationship between mean deviation and standard deviation in any type of distribution, including moderately non-symmetrical distributions. The ratio of mean deviation to standard deviation depends on the nature of the data and the degree of skewness in the distribution.

Conclusion
In conclusion, mean deviation and standard deviation are two measures of dispersion that are used to describe the variability of a dataset. Mean deviation is always less than or equal to standard deviation, but there is no fixed relationship between the two measures in any type of distribution, including moderately non-symmetrical distributions.

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