Weighted Mean and Survey Weights

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Calculate

Example: a poll heard 600 young people and 400 older people. Approval was 62% among the young and 40% among the older, but the young are only 35% of the population. What is the estimated approval? Leave the respondents blank for an ordinary weighted mean.

Values x_i One per group, separated by spaces or commas. Weights w_i In the same order; in a poll, each group's share of the population. Respondents per group (optional) Blank: an ordinary weighted mean, without the survey-weight calculation.

Step by step

What each term means

Weighted Mean (x̄_w): A mean in which some values count more than others. With equal weights, it becomes the simple mean.
Sum of the Weighted Values: Each value multiplied by its weight, added up. Values with a larger weight contribute more.
Sum of the Weights: Dividing by the total weight brings the result back to the scale of the values. That is why weights can be counts, percentages or fractions: only their proportions matter.