The impact of extreme observations on statistical measures is crucial for data analysis, especially in the context of the arithmetic mean, median, and mode. Here’s a detailed breakdown:

Arithmetic Mean
- The arithmetic mean is highly sensitive to extreme values (outliers).
- A single extreme value can significantly shift the mean, making it unrepresentative of the dataset.
- For instance, in the dataset {1, 2, 3, 100}, the mean is 26.5, greatly influenced by the outlier 100.

Median
- The median, defined as the middle value when data is ordered, is not affected by extreme values.
- In the same dataset {1, 2, 3, 100}, the median remains 2.5, reflecting the central tendency without the distortion caused by outliers.
- This makes the median a more robust measure of central tendency in skewed distributions.

Mode
- The mode, representing the most frequently occurring value, is also unaffected by extreme observations.
- If we take the dataset {1, 2, 2, 3, 100}, the mode is 2, which remains unchanged despite the extreme value of 100.
- Therefore, the mode is useful in understanding the commonality of data points, regardless of outliers.

Conclusion
- In summary, while the arithmetic mean is sensitive to extreme observations, both the median and mode provide a more accurate representation of central tendency in the presence of outliers.
- Understanding these differences is essential for effective data interpretation, particularly in statistical analysis relevant to UPSC examinations.