Question

Why is the Median considered a more robust measure of central tendency than the Mean when outliers are present?

Hint:

\textbf{Remember:} Outliers present → Use Median, not Mean.

Answer 1

Concept: Measures of central tendency describe the center of a dataset. However, their reliability depends on how sensitive they are to extreme values (outliers). Answer: The median is considered more robust than the mean because it is less affected by outliers or extreme values. Explanation:

The mean is calculated by adding all values and dividing by the total number of observations. A single very large or very small value can significantly shift the mean.
The median is the middle value when data is arranged in order. It depends only on the position of values, not their magnitude.
Therefore, extreme values do not strongly influence the median.
Example: Consider the dataset: \[ 2,\ 3,\ 4,\ 5,\ 100 \]

Mean $= \frac{2+3+4+5+100}{5} = 22.8$ (heavily affected by 100)
Median $= 4$ (represents the central value better)
Key Insight:

Mean → Sensitive to outliers
Median → Resistant to outliers
Conclusion: Because the median depends on the order of data rather than extreme values, it provides a more reliable measure of central tendency in datasets containing outliers.