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Weighted Average =
An average is a statistical measure used to represent a typical or central value in a data set. It is an essential tool for summarizing numerical information and gaining a better understanding of the overall trend in the data. In the academic context, averages are commonly used to assess student' performance in a course or subject, providing an overview of their achievements. Averages can be calculated in different ways, but the two most common types are the arithmetic mean and the weighted average.
The arithmetic mean is the simplest type of average. It is calculated by adding all the values together and dividing the total by the number of elements in the set. In essence, it represents the total sum of the values divided by their count. In other words, it can be considered a special case of the weighted average in which all values have equal weight. For example, if we have four values: 65, 70, 43, and 54, the arithmetic mean would be (65 + 70 + 43 + 54) / 4 = 58.
The weighted average, on the other hand, provides a more accurate measure by taking into account the relative importance of each value. Each value is multiplied by a specific weight or percentage, and the resulting products are then summed. This sum is divided by the total of the weights. This method is especially useful when some values contribute more to the final result than others, making it ideal for analyses that involve different levels of significance among data points.
If we define each value as Vi and its respective weight as Wi, then the formula to calculate the weighted average is as follows:
In this formula, Vi represents the individual values to be averaged (for example, grades obtained in different exams), and Wi are the specific weights assigned to each value (for example, the weighting percentage of an exam in the final course average). The numerator calculates the weighted sum of all values, and the denominator calculates the sum of all weights. Dividing the numerator by the denominator gives the weighted average.
This formula is useful for calculating grade averages, project evaluations, or any situation where certain elements in the data set need to be given more importance. Weighted averages offer a more accurate and fair view of performance when assessments are not equally significant.