Think & Reflect · Q4
Q.Out of Mean and Median, which one is more sensitive to outliers in data?
Tripura TbseTextbookSubjective· 2mImportance★★★★★est
100% · 20/20 Questions
You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.
Start your 14-day free trial to unlock the full solution →Out of the two, the mean is far more sensitive to outliers. Its formula sums every value, so one extreme observation pulls the whole average toward itself. The median looks only at the middle of the sorted data — an outlier sitting at either end barely affects which value is in the middle.
Why, from the formulas
- Mean = (sum of all values) / n → an outlier enters the sum at full strength. Make one value 100 cm larger and the mean rises by 100/n.
- Median = middle value of the sorted data → an outlier only occupies an end position in the sorted order; the middle element usually does not change at all.
A concrete demonstration with the class heights
Original data: mean = 101.33 cm, median = 102 cm. Now suppose one height was mis-recorded as 215 instead of 115:
| Measure | Original data | With outlier (115 → 215) | Shift |
|---|---|---|---|
| Mean | 101.33 cm | 112.44 cm | +11.11 cm |
| Median | 102 cm | 102 cm | 0 |
The sorted data with the outlier is 85, 90, 90, 100, 102, 110, 110, 110, 215 — the 5th value is still 102, so the median is untouched, while the mean jumped past every "typical" student's height.
import statistics
heights = [90, 102, 110, 115, 85, 90, 100, 110, 110]
with_outlier = [90, 102, 110, 215, 85, 90, 100, 110, 110] # one bad reading
print(statistics.mean(heights), statistics.median(heights))
print(round(statistics.mean(with_outlier), 2), statistics.median(with_outlier))
101.33333333333333 102
112.44 102
``` …
Unlock everything free for 14 days
- Full step-by-step solutions
- Concept-first explanations
- Methods, shortcuts & mistakes
- PYQ mapping + timed mock tests
Full access for 14 days. No credit card required.