Finding the mean from a table
The mean is found by adding up all the numbers and dividing by how many numbers there are.
To find the mean in this example, the total number of goals must be found and then divided by the number of games.
From the table, it can be seen that in 2 games no goals were scored. This makes a grand total of zero goals so far. The rest of the total amount of goals can be worked out in this way, by multiplying goals (\(x\)) by the frequency (\(f\)). Call this column \(fx\) (\(f\) multiplied by \(x\)).
| Number of goals (\(x\)) | Frequency (\(f\)) | \(fx\) | |
| 0 | 2 | \(0 \times 2 = 0\) | |
| 1 | 2 | \(1 \times 2 = 2\) | |
| 2 | 5 | \(2 \times 5 = 10\) | |
| 3 | 1 | \(3 \times 1 = 3\) | |
| Total | 10 | 15 |
| Number of goals (\(x\)) | 0 |
|---|---|
| Frequency (\(f\)) | 2 |
| \(fx\) | \(0 \times 2 = 0\) |
| Number of goals (\(x\)) | 1 |
|---|---|
| Frequency (\(f\)) | 2 |
| \(fx\) | \(1 \times 2 = 2\) |
| Number of goals (\(x\)) | 2 |
|---|---|
| Frequency (\(f\)) | 5 |
| \(fx\) | \(2 \times 5 = 10\) |
| Number of goals (\(x\)) | 3 |
|---|---|
| Frequency (\(f\)) | 1 |
| \(fx\) | \(3 \times 1 = 3\) |
| Total | |
|---|---|
| Number of goals (\(x\)) | |
| Frequency (\(f\)) | 10 |
| \(fx\) | 15 |
The total number of goals is 15. There were 10 football games so \(15 \div 10 = 1.5\).
The mean number of goals is 1.5 goals per game.
Remember to divide \(fx\) by the total of the frequencies, not by the amount of different items of data – the correct answer here is \(\frac{15}{10}\) not \(\frac{15}{4}\).