Consider the following statements: I. Mean and variance have the...

Let the unit of observation $x_i$ be $u$.

The mean is given by $\bar{x} = \dfrac{1}{n} \sum x_i$, which has the unit $u$.

The variance is given by $\sigma^2 = \dfrac{1}{n} \sum (x_i - \bar{x})^2$, which has the unit $u^2$. Thus, mean and variance have different units of measurement. Statement I is incorrect.

The mean deviation is given by $\dfrac{1}{n} \sum |x_i - \bar{x}|$, which has the unit $u$.

The standard deviation is given by $\sigma = \sqrt{\dfrac{1}{n} \sum (x_i - \bar{x})^2}$, which has the unit $\sqrt{u^2} = u$. Thus, mean deviation and standard deviation have the same unit of measurement. Statement II is correct.

Answer: II only