Question

Which measure of central tendency is most affected by extreme values (outliers)?

• A. Median
• B. Mode
• C. Mean
• D. Quartile

Hint:

{Mean is sensitive to outliers}, whereas {Median is more stable} when extreme values are present in the dataset.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to identify which statistical average changes significantly when there is a very high or very low value in the dataset.
Step 2: Detailed Explanation:
- Mean: Calculated by summing all values and dividing by the count ($ \text{Mean} = \frac{\sum x}{n} $). Since every single value is part of the calculation, one extreme outlier will pull the average toward it.
- Median: The middle-most value when data is sorted. It only cares about the position, not the magnitude of the outer values.
- Mode: The most frequent value. Outliers usually don't repeat often enough to become the mode.
Example: In the set $\{1, 2, 2, 3, 100\}$, the Mean is 21.6 (heavily influenced by 100), while the Median is 2.
Step 3: Final Answer:
The Mean is the measure most affected by extreme values.