How to Find the Score Needed for a Target Average

When the average so far falls short of a target, this finds what is still needed. Averages cannot be added or subtracted directly, so both are turned into totals first.

$n$ is the number of attempts so far, $A$ the average over them, $T$ the target average, $m$ the attempts remaining and $S$ the total still needed. Dividing $S$ by $m$ gives the score needed per attempt, which is shown as well.

Example

After three attempts averaging 72, two remain and the target is 80. Across all five, $5 \times 80 = 400$ is needed in total, and $3 \times 72 = 216$ has been scored. The difference, $400 - 216 = 184$, is what the last two must bring in, or $184 \div 2 = 92$ each.

Do not subtract one average from the other

Making up the 8 point gap between 72 and 80 is not enough. The three attempts already taken fall short as well, by $8 \times 3 = 24$ points in total, and that shortfall has to be carried by the attempts that remain. Spread over two, it adds 12 to each, giving $80 + 12 = 92$. The fewer attempts left, the heavier each one becomes.

Notes

The score needed per attempt can come out above full marks, which means the target is out of reach in the attempts remaining.

The attempts remaining must be a whole number of at least 1. The attempts so far may be 0.