In a uniform distribution, how is the variance calculated?

In a uniform distribution, how is the variance calculated?

• A. by using the range of values
• B. by averaging the maximum and minimum values
• C. by squaring the difference between max and min values
• D. by dividing the square of the range by a constant

Answer: (D)

In a uniform distribution, the variance is calculated using the range of values. For a continuous uniform distribution defined by a minimum value \( a \) and a maximum value \( b \), the variance is given by the formula: \[ \text{Variance} = \frac{(b - a)^2}{12} \] This means that the variance is directly related to the square of the range (which is \( b - a \)) divided by a constant, specifically 12 for a continuous uniform distribution. This correctly describes why the option referring to dividing the square of the range by a constant provides the accurate method for calculating the variance in a uniform distribution. Understanding this relationship allows for a straightforward calculation of variance based on the known maximum and minimum values of the distribution.

In a uniform distribution, the variance is calculated using the range of values. For a continuous uniform distribution defined by a minimum value ( a ) and a maximum value ( b ), the variance is given by the formula:

[

\text{Variance} = \frac{(b - a)^2}{12}

]

This means that the variance is directly related to the square of the range (which is ( b - a )) divided by a constant, specifically 12 for a continuous uniform distribution.

This correctly describes why the option referring to dividing the square of the range by a constant provides the accurate method for calculating the variance in a uniform distribution. Understanding this relationship allows for a straightforward calculation of variance based on the known maximum and minimum values of the distribution.