A frequency table is a list in short form
A row "2 pets, frequency 7" means the value 2 appears 7 times. To find the mean, multiply each value by its frequency, add these up, then divide by the total frequency.
| Number of pets | Frequency | Pets × frequency |
|---|---|---|
| 0 | 5 | 0 |
| 1 | 8 | 8 |
| 2 | 4 | 8 |
| 3 | 3 | 9 |
| Total | 20 | 25 |
Mean = 25 ÷ 20 = 1.25 pets. The mode is the value with the highest frequency (1 pet). The median is the middle of all 20 values: the 10th and 11th are both 1, so the median is 1.
Grouped data: use the midpoints
When the data are in classes such as 10 < t ≤ 20, you do not know the exact values. Use the midpoint of each class (15 here) to stand for every value in it. The answer is an estimate of the mean.
- Midpoints: 5, 15, 25 with frequencies 4, 10, 6
- Σ(f × midpoint) = 20 + 150 + 150 = 320
- Estimate of the mean = 320 ÷ 20 = 16
The modal class has the highest frequency. The class that contains the median is the one where the running total first passes half way.
Divide by the right number
Divide by the total frequency (here 20), never by the number of rows or classes. A mean that comes out bigger than the largest value, or smaller than the smallest, means something has gone wrong.