Average
The arithmetic mean, the sum-count-average triangle, how an average shifts when a value is added or removed, and why average speed over equal distances is not the mean of the two speeds.
What you will be able to do
- Move freely between sum, count and average.
- Update an average when a value is added, removed or replaced.
- Use the assumed-mean (deviation) shortcut to average quickly.
- Compute average speed correctly for equal distances and for equal times.
What is inside this lesson
- 1What an average is
- 2The sum, count, average triangle
- 3When a value is added, removed or replaced
- 4Worked example: a value removed
- 5Worked example: the score needed to lift an average
- 6Worked example: average speed over equal distances
- 7Common mistakes
- 8Quick revision
- 9Practice
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What an average is
The average, or arithmetic mean, of a set of numbers is their sum divided by how many there are. It is the single value that could replace every member of the set without changing the total.
That last idea is the useful one for exams. If the average of 12 innings is 48, the batsman's total is 48 times 12, that is 576, regardless of the individual scores. Most average questions are really questions about the total, reached through the average.
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