A report says "the average package offered at our campus is ₹12 LPA", but most students you know got much less. Explain how this can happen using mean, median and skewness. Which measure would you report, and what else would you show?
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How it happens. The mean adds up every value and divides by the count, so a few very large offers pull it upward. The median is the middle value when the offers are sorted, so it does not care how large the top offers are.
Toy example with five offers in LPA: 4, 5, 5, 6, 40. Mean = 60/5 = 12. Median = 5. Four of the five students earn far below the "average".
Skewness describes the asymmetry of a distribution.
- Right (positive) skew: a long tail of large values. Usually mean > median. Incomes, house prices and package data are typical examples.
- Left (negative) skew: a long tail of small values, such as marks on an easy exam. Usually mean < median.
- Symmetric: mean ≈ median, as for heights.
(The mean/median rule usually holds, but there are exceptions. Plot the data.)
What to report for skewed data
- The median as the typical value, plus the interquartile range (Q1–Q3) for spread. Both are robust to outliers.
- Percentiles (such as the 25th, 50th, 75th and 90th), or a histogram or box plot.
- The count: how many students were placed, out of how many eligible. An average over placed students only hides the unplaced ones.
- Report the mean too if needed, but label it clearly.
When the mean is the right choice: for roughly symmetric data, and when totals matter (total payroll = mean × count). Many statistical methods are built on the mean.
Mode: the most frequent value. It is useful for categories ("the most common branch") or a clearly dominant value.
Outliers are not always errors. Check data-entry mistakes (an extra zero), but genuine extreme values should be reported, not silently deleted. Use the median or a log scale so they do not distort the picture.
Original UniCircle question. Last reviewed 22 Oct 2026.