Relative frequency
Relative frequencyHow many times a value occurs. or experimental probabilityThe extent to which something is likely to be the case. is calculated from the number of times an event happens, divided by the total number of trials in an actual experiment.
The theoretical probability of getting a head when you flip a fair coin is \(\frac{1}{2}\), but if a coin was actually flipped 100 times you may not get exactly 50 heads, although it should be close to this amount.
If a coin was flipped a hundred times, the amount of times a head actually did appear would be the relative frequency, so if there were 59 heads and 41 tails the relative frequency of flipping a head would be \(\frac{59}{100}\) (or 0.59 or 59%).
Relative frequency is used when probability is being estimated using the outcomes of an experiment or trial, when theoretical probability cannot be used.
For example, when using a biased dice, the probability of getting each number is no longer \(\frac{1}{6}\). To be able to assign a probability to each number, an experiment would need to be conducted. From the experimental results, the relative frequency could be calculated.
The more times that an experiment has been carried out, the more reliable the relative frequency is as an estimate of the probability.
Example
Ella rolls a dice and records the number of times she scores a six. Find the relative frequency that Ella rolls a six on her dice.
| Number of rolls | 10 | 20 | 30 | 40 | 50 |
| Total number of sixes | 2 | 3 | 6 | 8 | 9 |
| Number of rolls |
|---|
| 10 |
| 20 |
| 30 |
| 40 |
| 50 |
| Total number of sixes |
|---|
| 2 |
| 3 |
| 6 |
| 8 |
| 9 |
Ella’s results will give different estimates of the probability, depending on which total is selected.
For example, in the first 10 rolls, the relative frequency of scoring 6 is \(\frac{2}{10} = 0.2\), but in the first 20 rolls, the relative frequency of scoring 6 is \(\frac{3}{20} = 0.15\).
The most accurate estimate of the probability is found by using the highest number of rolls, which gives \(\frac{9}{50} = 0.18\)
