What is the equation for variance in a uniform distribution?

In a uniform distribution, where the values are evenly distributed between two parameters, (a) (the minimum) and (b) (the maximum), the formula for variance is derived from the properties of the distribution. Variance measures the spread of the distribution, indicating how much the values deviate from the mean.

The correct formula for variance in a uniform distribution is given by (\text{Var}(x) = \frac{(b - a)^2}{12}). This equation shows that variance is based on the square of the difference between the upper and lower bounds of the distribution, divided by 12. The factor of 12 arises from the calculation of the second moment about the mean and provides a standardized way to express the variability of the uniform distribution.

This formulation reflects that as the interval between (a) and (b) increases, the variance increases, depicting greater dispersion in the distribution of values. It is essential to recognize that in a uniform distribution, all outcomes between (a) and (b) are equally likely, hence leading to this specific variance formula. The other options do not represent the characteristics necessary for the variance of a uniform distribution.