Step 1: Understanding the Question:
The question asks to identify the most robust and preferred measure of central tendency for a dataset containing extreme values or outliers.
Step 2: Analysis of Measures of Central Tendency:
- Mean (Arithmetic Average): Sum of all values divided by the number of values.
- Median (Middle Value): The physical middle data point when the data is sorted in ascending or descending order.
- Mode (Most Frequent Value): The value that appears most often in the dataset.
Step 3: Detailed Explanation:
- Let us analyze how outliers affect these measures using a simple numerical example:
- Suppose we have five data points representing salaries: 20, 22, 25, 28, 500 (where 500 is an extreme outlier).
- Let's compute the Mean:
\[ \text{Mean} = \frac{20 + 22 + 25 + 28 + 500}{5} = \frac{600}{5} = 120 \]
The mean of 120 is not a good representation of the central value, as four out of five data points are far below 120. The outlier has heavily skewed the mean upward.
- Let's compute the Median (middle element of sorted data):
The sorted data is 20, 22, [25], 28, 500. The middle value is 25.
This value (25) is a much better representation of the central tendency of the group, and it remains completely unaffected by the extreme value of 500.
- Because the median relies purely on the ordinal position of values rather than their magnitude, it is highly resistant (robust) to outliers.
Step 4: Final Answer:
When a dataset contains outliers, the Median is the preferred measure of central tendency for finding the central value.
Hence, option (B) is the correct choice.