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

Why Median is More Robust than Mean in Presence of Outliers:

The median is considered a more robust measure of central tendency than the mean when outliers or extreme values are present in a dataset. This is due to the way each measure is calculated and how they respond to extreme observations.

Key Points:
1️⃣ Definition of Mean: The mean is the arithmetic average of all values in a dataset, calculated by summing all values and dividing by the number of observations.
2️⃣ Definition of Median: The median is the middle value of a dataset when it is arranged in ascending or descending order. If the dataset has an even number of observations, it is the average of the two middle values.

Effect of Outliers:
• Outliers are extremely high or low values that differ significantly from the majority of data points.
• The mean is sensitive to every value, so outliers can drastically shift its value.
• The median depends only on the middle position of data and is not affected by extreme values at the ends.

Example:
Dataset without outlier: 10, 12, 14, 16, 18
- Mean = (10+12+14+16+18)/5 = 14
- Median = 14

Dataset with an outlier: 10, 12, 14, 16, 100
- Mean = (10+12+14+16+100)/5 = 30.4
- Median = 14
Here, the mean is greatly affected by the outlier (100), while the median remains the same, accurately representing the central tendency of the majority of the data.

Conclusion:
The median is more robust than the mean because it is resistant to the influence of outliers, making it a better measure of central tendency in datasets with extreme values.