Which measure is least affected by outliers in a numerical dataset?MaximumMeanMinimumMedianSee all questionsBackNext question

Step 1: Break Down the Problem

To determine which measure is least affected by outliers, we need to analyze the behavior of the following four statistical measures: maximum, mean, minimum, and median.

Step 2: Relevant Concepts

1. Mean: The average of all data points. Highly sensitive to outliers.
2. Median: The middle value in a sorted list of numbers. Less sensitive to outliers as it depends only on the rank of values, not their magnitude.
3. Maximum: The highest value in the dataset. It can be significantly impacted by outliers.
4. Minimum: The lowest value in the dataset. It is also affected by outliers.

Step 3: Analysis and Detail

• Mean: If an outlier is extremely high or low, it will pull the mean in its direction, making it a poor representation of the dataset.
• Median: By sorting the dataset, the median remains unchanged as long as the number of observations is even or only slightly altered if the number of observations is odd. Thus, the median is not swayed by extreme values.
• Maximum and Minimum: Both are direct values from the dataset, and thus any extreme outlier will directly affect these measures.

Step 4: Verify and Summarize

Given the analyses above, it is clear that the median remains stable despite extreme values influencing the maximum, minimum, and mean.

Final Answer

The measure least affected by outliers in a numerical dataset is the Median.