Combine totals correctly and see how changing group proportions can reverse a comparison.
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First lesson in this subject: Read data before calculating
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One group has 2 observations with mean 10; another has 8 with mean 20. Their totals are 20 and 160, so the combined mean is 180/10 = 18.
Averaging the two means gives 15, which gives the groups equal weight despite their different sizes. Multiply each mean by its group size, add the totals, then divide by the total count.
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First lesson in this subject: Read data before calculating
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Practice · Change the group sizes and watch the overall winner change.
Book · Read distributions, question samples, and explore how groups and outliers change a conclusion.
Previous lesson · Distinguish chance differences between random samples from systematic selection bias.
Next lesson · Investigate influential observations while keeping correlation separate from causation.
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