Which component is used to calculate the mean by weighting each observed outcome by its what?

Which component is used to calculate the mean by weighting each observed outcome by its what?

• A. Dollar value of the outcome
• B. Credibility factor
• C. Adjusted modification factor
• D. Relative frequency

Answer: (D)

The mean that reflects how often each outcome occurs uses relative frequency as the weight. Relative frequency tells you how likely or how often a particular observed value appears in the data, so it’s the natural weight for averaging those values. When you compute a weighted mean, you multiply each observed value by how often it occurs (its weight), sum those products, and divide by the total number of observations. If you use relative frequencies as weights, the sum of weights is 1, and the mean becomes the sum of each value times its relative frequency. For example, if you have values 5, 10, and 20 that occur with frequencies 1, 3, and 2, the weighted mean is (5*(1/6) + 10*(3/6) + 20*(2/6)) = 75/6 = 12.5. Dollars or magnitudes of outcomes aren’t weights in this approach, credibility factors and modification factors relate to other concepts (credibility theory and adjustments in pricing), and they don’t serve as the weighting basis for a mean in this context. The relative frequency is the correct weighting component because it directly represents how often each observed outcome occurs.

The mean that reflects how often each outcome occurs uses relative frequency as the weight. Relative frequency tells you how likely or how often a particular observed value appears in the data, so it’s the natural weight for averaging those values.

When you compute a weighted mean, you multiply each observed value by how often it occurs (its weight), sum those products, and divide by the total number of observations. If you use relative frequencies as weights, the sum of weights is 1, and the mean becomes the sum of each value times its relative frequency. For example, if you have values 5, 10, and 20 that occur with frequencies 1, 3, and 2, the weighted mean is (5*(1/6) + 10*(3/6) + 20*(2/6)) = 75/6 = 12.5.

Dollars or magnitudes of outcomes aren’t weights in this approach, credibility factors and modification factors relate to other concepts (credibility theory and adjustments in pricing), and they don’t serve as the weighting basis for a mean in this context. The relative frequency is the correct weighting component because it directly represents how often each observed outcome occurs.