A
You’re right — BMI is typically not normally distributed in most real populations.
Here’s why, and what that means in practice:
Why BMI isn’t normal
Right-skewed distribution: There’s a hard lower bound (you can’t have negative BMI), but no strict upper bound. A smaller number of very high BMIs pull the tail to the right.
Population heterogeneity: Mixing ages, sexes, ethnicities, and health statuses creates multiple sub-patterns instead of one clean bell curve.
Biological + social factors: Diet, activity, socioeconomic status, and disease don’t affect BMI symmetrically.
So instead of a nice bell shape, BMI usually looks skewed, sometimes even bimodal.
Why this matters
If BMI isn’t normal, then:
The mean > median (mean gets pulled upward)
t-tests, ANOVA, linear regression assumptions may be violated
Confidence intervals and p-values can be misleading if you don’t adjust
What to do instead
Depending on your goal:
Descriptive stats
Report median + IQR instead of mean ± SD
Comparisons
Use non-parametric tests (Mann–Whitney, Kruskal–Wallis)
Or analyze BMI categories (underweight / normal / overweight / obese)
Modeling
Transform BMI (e.g., log(BMI))
Use robust regression
Or model a related measure (e.g., waist circumference) if appropriate
Large samples note
With big datasets, parametric tests can still work due to the Central Limit Theorem, but interpretation still needs care.
If you want, tell me what you’re doing with BMI (paper, regression, hypothesis test, clinical report), and I’ll suggest the cleanest statistical approach for that use case.