# Global sensitivity of mean and variance in differential privacy?

Please explain me why global sensitivity of a mean or variance queries will be

(b-a)/n


and

(b-a)^2/n


where b is the upper bound of the data and a is the lower bound?

The global sensitivity is defined as $$\max_{M,M'\text{ neighboring databases}}|f(M)-f(M')|$$, where $$f$$ is your function, and "neighboring databases" typically mean "differing in at most one element". Given the formulas you give, I assume that your in use case, "neighboring" means "$$M$$ and $$M'$$ both have $$n$$ elements, and $$n-1$$ elements in common".
When $$f$$ is the average, assuming that all elements are between $$a$$ and $$b$$, the maximum is reached when the only differing element between $$M$$ and $$M'$$ is $$a$$ in one of the databases and $$b$$ in the other. In that case, you can easily verify that $$|f(M)-f(F')|=\frac{b-a}{n}$$, and similarly for when $$f$$ is the variance.