What is skewness, and what does it tell you about the mean and median?
Skewness measures how lopsided a distribution is. In a right-skewed distribution a long tail of large values pulls the mean above the median; in a left-skewed one the mean falls below the median.
Explain it simply
Picture the daily spend of customers at a canteen. Most spend 40 to 80 rupees, but a few groups order for 2,000. The bulk of the data sits on the left and a long tail stretches to the right. That is right (positive) skew.
A symmetric distribution, like heights of adults, has skewness near 0 and the mean is close to the median.
Example
import pandas as pd
s = pd.Series([2, 3, 3, 4, 4, 4, 5, 5, 30])
print(s.mean()) # 6.666666666666667
print(s.median()) # 4.0
print(s.skew() > 0) # TrueOne value, 30, drags the mean to about 6.67 while the median stays at 4. The mean is greater than the median, the signature of right skew.
| Shape | Skewness | Usual order |
|---|---|---|
| Right-skewed | positive | mean > median |
| Symmetric | about 0 | mean about median |
| Left-skewed | negative | mean < median |
What to say in the interview
"Skewness is the third standardised moment and measures asymmetry. Positive means a long right tail, so mean exceeds median. For income, prices or waiting times I report the median, and a log transform often makes such data closer to symmetric before modelling."
Common mistakes
- Reading the direction from where the bulk sits. The name comes from the tail, not the hump.