Question

Which of the following measures of central tendency is not affected by presence of outliers?

• A. Arithmetic mean
• B. Harmonic mean
• C. Median
• D. Geometric mean

Hint:

When analyzing highly skewed data (like household incomes or real estate prices) containing extreme outliers, always prefer the median over the mean for a more realistic measure of central tendency.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Measures of central tendency summarize a dataset using a single representative value.
The sensitivity of these measures to extreme values (outliers) varies depending on how they are calculated.

Step 2: Detailed Explanation:
The arithmetic mean, geometric mean, and harmonic mean are mathematical averages.
Their calculations incorporate the numerical value of every single observation in the dataset.
Consequently, if there are extreme values (outliers) at either end of the distribution, these means will be pulled toward the outliers, distorting the representation of central tendency.
On the other hand, the median is a positional average.
It is defined as the middle value when the data points are arranged in ascending or descending order.
Because the median depends solely on the rank or position of the observations rather than their actual numerical magnitudes, changing the extreme values does not affect its value.
Thus, the median is highly robust and remains unaffected by the presence of outliers.

Step 3: Final Answer:
The measure of central tendency not affected by outliers is the Median.