Which statistical mean is not effected by marginal values ?

Q: Which statistical mean is not effected by marginal values ?

Which statistical mean is not effected by marginal values ?

Question

Accepted Answer

The correct option is 1:

M (Median) is the positional average, meaning it is determined by the position of the value in a dataset after it has been arranged in ascending or descending order. The median simply divides the data into two equal halves. Because its calculation relies only on the central value(s) and ignores the exact magnitude of the extreme scores (marginal values, or outliers), it is highly resistant to their influence. Therefore, if a dataset contains extremely high or extremely low values, the median remains a reliable measure of central tendency, making it an ideal choice for skewed distributions.

The incorrect option is 2:
X (Arithmetic mean) is the average found by summing all values and dividing by the count of observations. Since every single value in the dataset contributes directly to the sum, the Arithmetic Mean is acutely sensitive to marginal or extreme values (outliers), which can pull the mean significantly in their direction.

The incorrect option is 3:
Z (Mode) is defined as the value that appears most frequently in a dataset. While the mode is generally not affected by a single extreme observation, a large enough cluster of extreme values could potentially create a new modal peak, but in the context of typical measures of central tendency affected by magnitude changes, the mean is the better contrast to the median. However, in the provided options, the mode is also a positional average like the median and is generally robust against typical outliers, but the primary and most sensitive measure among the choices, and the one most affected by every value, is the arithmetic mean. Since the median is the explicitly correct answer for robustness against *all* marginal values, the mode is incorrect because it is not the best answer in this context, although it shares a similar property of robustness to the median compared to the mean.

The incorrect option is 4:
H. M. (Harmonic Mean) is a specialized average used primarily for rates and ratios. Like the Arithmetic Mean, the calculation of the Harmonic Mean uses the value of every observation in the dataset (specifically their reciprocals). Due to this dependence on every value, it is also highly affected by marginal, particularly low, values, and is thus not the correct choice.