In any discrete series (when all values are not same) the relationship between M.D. about mean and S.D. is (a) M.D. = S.D. (b) M.D. \(\leq\) S.D. (c) M.D. < S.D. (d) M.D. \(\leq S . D\).

The Mean Deviation (M.D.) is a measure of dispersion that calculates the average distance of each value in a dataset from the mean. The formula for the M.D. about the mean for a discrete series is: \(M.D. = \frac{1}{N}\sum_{i=1}^N \lvert x_i - \overline{x} \rvert\), where \(N\) is the number of data points, \(x_i\) is an individual data point, and \(\overline{x}\) is the mean of the dataset.

The Standard Deviation (S.D.) is also a measure of dispersion that calculates the average distance of each value in a dataset from the mean but weighs them according to their distribution. The formula for the S.D. of a discrete series is: \(S.D. = \sqrt{\frac{1}{N}\sum_{i=1}^N (x_i - \overline{x})^2}\), with the same notations as before.

We can compare the formulas for M.D. and S.D. by considering the difference in the method used to calculate the average distance from the mean. M.D. calculates the average of the absolute differences from the mean, while S.D. calculates the square root of the average of the squared differences from the mean. Since squaring a value (in cases of \(x_i - \overline{x} > 0\)) always results in a non-negative value that could be larger than the original value, and squaring a value (in cases of \(x_i - \overline{x} < 0\)) results in non-negative value larger than the original absolute value, it is clear that S.D. will always be greater than or at least equal to M.D. Hence, the relationship between Mean Deviation and Standard Deviation is: \(M.D. \leq S.D.\) So, the correct option is: (b) M.D. \(\leq\) S.D.