Relative Frequency and Carrying out Experiments (Leaving Cert Mathematics): Revision Notes

Relative Frequency and Carrying out Experiments

Relative Frequency

Relative frequency is the proportion of times an event occurs relative to the total number of trials in an experiment. It is used to estimate probabilities, especially when dealing with experimental or observed data.

The formula for relative frequency is:

$$\text{Relative Frequency} = \frac{\text{Number of times the event occurs}}{\text{Total number of trials}}$$

Key points:

• Estimation of Probability: Relative frequency provides an estimate of the likelihood of an event.
• Long-Run Stability: As the number of trials increases, the relative frequency tends to stabilise and approach the true probability of the event.

Carrying Out Experiments

Experiments are conducted to collect data and observe outcomes to determine probabilities or validate hypotheses. When carrying out experiments:

1. Define the Event:

• Specify the event of interest (e.g., flipping a coin to get "heads").

2. Perform the Experiment:

• Repeat the experiment multiple times under similar conditions.

3. Record Outcomes:

• Count the occurrences of the event of interest and the total number of trials.

4. Calculate Relative Frequency:

• Use the formula above to compute the relative frequency.

Worked Example

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Repeating Experiments

Repeating experiments increases accuracy:

• A single experiment may produce results influenced by random variation.
• Repeating the experiment and averaging the results ensures better estimates of probabilities.

Law of Large Numbers:

The relative frequency of an event converges to the theoretical probability as the number of trials increases.

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