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When data are summarised into classes, their exact values are lost. There is no way of knowing whether the original observations were near the bottom of the class, the top of the class or evenly spread out.

Assuming that all the observations that fall into a particular class take the midpoint value is a reasonable approximation. It is the maximum likelihood unbiased estimate. It also sets the variance within each class to 0.

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Q: Why is class midpoint in statistical formulas important?
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