Weightaveraged
Weightaveraged refers to the process of computing a weighted average, where each value is multiplied by a corresponding weight that reflects its relative importance or frequency before the average is taken. The standard formula for a weightaveraged value of a set of values x1, x2, ..., xn with weights w1, w2, ..., wn is:
(weightaveraged) = (sum over i of w_i * x_i) / (sum over i of w_i)
If the weights are nonnegative and normalized so that their sum equals 1, the denominator is 1
- Weights determine influence: larger weights give more influence to their corresponding values.
- Relation to arithmetic mean: the simple unweighted average is a special case with equal weights.
- Flexibility: weights can reflect sample size, measurement reliability, probability, or prior information.
- In survey analysis, weights adjust for sampling design or nonresponse.
- In finance, weighted averages summarize prices or returns when some observations carry more significance.
- In data smoothing and signal processing, weighted averages form moving averages with nonuniform weighting, such as
- In machine learning and ensemble methods, predictions can be combined with weights representing confidence or performance.
- Weights should usually be nonnegative; negative weights can yield counterintuitive results.
- Denominators equal to zero render the weightaveraged value undefined.
- Depending on context, weights may be fixed or updated iteratively as new data arrive.