Mean
The mean is the most commonly used measure of average. If you ask someone to find the average, this is the method they are likely to use.
Kieran's results were:
\(10, 14, 10, 12, 11, 10, 11, 12, 10, 11, 9, 12\)
To calculate the mean, add the numbers together and divide the total by the amount of numbers. The mean for this example is:
\(\frac{10+14+10+12+11+10+11+12+10+11+9+12}{12}\)
\(= \frac{132}{12}\)
\(= 11\, tracks\)
Question
A joiner bought seven packets of nails. The number of nails in each packet was as follows:
\(8, 7, 6, 7, 9, 8, 7\)
Calculate the mean number of nails per packet. (Give your answer to two decimal places)
\(Total\, nails = 8+7+6+7+9+8+7 = 52\)
\(Number\, of\, packets = 7\)
\(Mean = \frac{52}{7} = 7.43\)
Finding the mean from a frequency table
Putting Kieran’s results (data) into a frequency table looks like this.
| Number of tracks on album | Number of albums (frequency) |
| 9 | 1 |
| 10 | 4 |
| 11 | 3 |
| 12 | 3 |
| 13 | 0 |
| 14 | 1 |
| Number of tracks on album | 9 |
|---|---|
| Number of albums (frequency) | 1 |
| Number of tracks on album | 10 |
|---|---|
| Number of albums (frequency) | 4 |
| Number of tracks on album | 11 |
|---|---|
| Number of albums (frequency) | 3 |
| Number of tracks on album | 12 |
|---|---|
| Number of albums (frequency) | 3 |
| Number of tracks on album | 13 |
|---|---|
| Number of albums (frequency) | 0 |
| Number of tracks on album | 14 |
|---|---|
| Number of albums (frequency) | 1 |
Kieran could have found the mean of his results by using this method.
| Number of tracks on album | Number of albums (frequency) | Tracks x frequency |
| 9 | 1 | 9 |
| 10 | 4 | 40 |
| 11 | 3 | 33 |
| 12 | 3 | 36 |
| 13 | 0 | 0 |
| 14 | 1 | 14 |
| Total = 12 | Total = 132 |
| Number of tracks on album | 9 |
|---|---|
| Number of albums (frequency) | 1 |
| Tracks x frequency | 9 |
| Number of tracks on album | 10 |
|---|---|
| Number of albums (frequency) | 4 |
| Tracks x frequency | 40 |
| Number of tracks on album | 11 |
|---|---|
| Number of albums (frequency) | 3 |
| Tracks x frequency | 33 |
| Number of tracks on album | 12 |
|---|---|
| Number of albums (frequency) | 3 |
| Tracks x frequency | 36 |
| Number of tracks on album | 13 |
|---|---|
| Number of albums (frequency) | 0 |
| Tracks x frequency | 0 |
| Number of tracks on album | 14 |
|---|---|
| Number of albums (frequency) | 1 |
| Tracks x frequency | 14 |
| Number of tracks on album | |
|---|---|
| Number of albums (frequency) | Total = 12 |
| Tracks x frequency | Total = 132 |
Then divide the two as follows:
\(Mean = \frac{132}{12} = 11\, tracks\)
