In a perfectly symmetrical distribution, such as a normal distribution, the mean, median, and mode are all equal. Therefore, if you have a symmetrical distribution with a mean (μ) of 30, the mode is also 30.
To elaborate, the mode is the value that appears most frequently in a data set. In cases of perfect symmetry, every value around the mean is balanced, which means that both the peak of the distribution (the mode) and the center (the mean) coincide. This property is what makes the normal distribution particularly useful in statistics, as it allows for a clear understanding of data trends and probabilities.
In conclusion, for a perfectly symmetrical distribution where the mean is 30, the mode is unequivocally 30 as well.