If third moment about mean is zero, distribution is:

The third moment about the mean is a statistical measure used to quantify the skewness of a probability distribution. Skewness indicates the asymmetry of the distribution of data points around its mean. A foundational fact is that for a perfectly symmetrical distribution, the data points are evenly balanced on both sides of the mean. Consequently, the sum of the cubed deviations from the mean, which constitutes the third moment, will cancel out to zero. Therefore, if the third moment about the mean is zero, the distribution is unequivocally symmetrical. Conversely, a positively skewed distribution, where the tail extends to the right, would have a positive third moment, indicating more extreme positive deviations. A negatively skewed distribution, with its tail extending to the left, would yield a negative third moment due to more extreme negative deviations. The option 'None of these' is incorrect because symmetry is precisely defined by this statistical property.