Finding a Missing Value Given the Mean

A mean is just a total divided by a count. That means the reverse works too: count times mean gives you back the total. Once you have the total, a missing value stops being mysterious — it's just whatever is left after you subtract every value you already know. This is why one missing score, with everything else given, is never a guess. It's an equation with exactly one unknown.

The mechanism is always the same three steps. First, multiply the mean by the number of values to get the required sum. Second, add up the values you already have. Third, subtract that sum from the required total — the difference is the missing value. If the missing value is unknown in more than name (a letter like x sitting in the list), you do the same subtraction, but leave the answer as an expression rather than a number.

This sits next to weighted averages on the test, and the two get confused. A plain mean treats every value equally, so the 'total = count times mean' trick applies directly. A weighted average gives some values more pull, so you'd multiply each value by its weight before adding. Spotting which kind of average a question describes — equal weight or not — decides whether this shortcut even applies.