Weighted Mean = (Σ (value × weight) ) / Σ (weight)

The weighted mean proves instrumental when working with data containing values with unequal significance or when certain values better represent the population.

Grades and Coursework: The education sector frequently employs the weighted mean to determine a student's overall course grade, given different assignments or exams carry distinct weights towards the final grade.

Finance and Investment: In the realm of finance, the weighted mean assists in calculating elements like the weighted average cost of capital (WACC) or determining portfolio returns based on the proportion of each investment in the portfolio.

Survey Data Analysis: Analysts and researchers working with survey data use the weighted mean to account for discrepancies in response rates or representation across demographic groups.

Incorporates Importance: The weighted mean acknowledges the relative importance or frequency of each dataset value, hence offering a more precise depiction of the overall population or distribution.

Reduced Bias: Weight assignment to different values in the weighted mean can curtail potential biases that might result from uneven sampling or inconsistent response rates.

More Accurate Estimates: When some values prove more representative or reliable than others, the weighted mean can yield more precise estimates of central tendency than the arithmetic mean.

Subjectivity in Assigning Weights: Allocating appropriate weights to each value can be subjective, often necessitating expert knowledge or assumptions regarding the values' relative importance.

Sensitive to Extreme Weights: The weighted mean can be heavily swayed by extreme weights, potentially resulting in skewed results if the weights do not correctly denote the true importance or frequency of the values.

Weighted Mean: The weighted mean accounts for the relative importance or frequency of each dataset value, rendering it more suitable when values possess varying degrees of significance or representation.

Arithmetic Mean: The arithmetic mean treats all values with equal importance by summing them and dividing by the total count. This method is preferable when values hold equal significance or when no details are accessible regarding the relative importance or frequency of values.

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