A distribution shows which values occur and how often. Its shape — symmetric, skewed, one peak or two — guides which statistics you should use.
Why it matters
The shape tells you whether the mean is trustworthy and whether a normal-based test is reasonable.
Key ideas
- Symmetric: mean ≈ median
- Right-skewed: long tail to the high side, mean > median
- Left-skewed: long tail to the low side, mean < median
- Two peaks may mean two hidden groups
- Skewness near 0 suggests symmetry
- Always look, don't rely on one number
Real-life research example
Time to recover from fever is usually right-skewed: most recover in 3 days, a few take two weeks.
When to use
- Before choosing mean/SD or median/IQR, and before a parametric test
When NOT to use
- Don't call data normal only because the sample is large
- Don't ignore a second peak
Mini example
Data: 2, 3, 3, 3, 4, 4, 5, 20 → skewness is clearly positive
Quick takeaway
Look at the shape first. It chooses your summary and your test.
Try it yourself
Type a right-skewed list (a few small numbers and one or two large) and a symmetric list. Compare skewness, mean and median in each.
Model answer
In the skewed list, skewness is positive and the mean is above the median. In the symmetric list, skewness is near zero and mean ≈ median.