Expected frequency (Edexcel GCSE Statistics): Revision Notes
Expected frequency
What is expected frequency?
Expected frequency is a way of predicting how many times you would expect an event to happen when you repeat an experiment a certain number of times. It's important to understand that this is what we expect to happen - it's not necessarily what will actually happen in real life!
The key idea is that if you know the probability of an event occurring, you can use this to predict the expected number of times it will happen over many trials.
The expected frequency formula
The formula for calculating expected frequency is straightforward:
Expected frequency of event A = P(A) × number of trials
Where:
- P(A) is the probability of event A happening
- Number of trials is how many times you repeat the experiment
This formula allows you to make predictions about what should happen when probability meets the real world.
Understanding probability for calculations
Before calculating expected frequency, you need to be able to find the probability of an event. For equally likely events:
Probability of an event = number of successful outcomes ÷ total number of possible outcomes
For example, with a fair six-sided dice, each number from 1 to 6 has an equal chance of being rolled. If you want to find the probability of rolling a number greater than 4, you would identify that there are 2 successful outcomes (5 and 6) out of 6 possible outcomes, giving a probability of 2/6 or 1/3.
Worked example: Dice rolling
Let's work through a complete expected frequency problem step by step:
Problem: A fair six-sided dice is rolled 100 times. Work out an estimate for the number of times you would expect to roll a number greater than 4.
Step 1: Find the probability of the event
- Numbers greater than 4 are: 5 and 6
- That's 2 successful outcomes out of 6 possible outcomes
- P(number > 4) = 2/6 = 1/3
Step 2: Apply the expected frequency formula
- Expected frequency = P(A) × number of trials
- Expected frequency = 1/3 × 100
- Expected frequency = 33.33...
Step 3: Round to a sensible answer
- Since we can't have a fraction of a roll, we round to 33
- You would expect a number greater than 4 to be rolled approximately 33 times
Important points to remember
It's a prediction, not a guarantee: Expected frequency tells you what should happen on average, but actual results will usually be different. If you actually rolled the dice 100 times, you might get 29, 35, or any other reasonable number near 33.
Rounding: Always round your final answer to a whole number when dealing with expected frequency, as you can't have partial events.
Check your probability: Make sure your initial probability calculation is correct - if this is wrong, your expected frequency will be wrong too.
Common exam tips
- Don't over-complicate fractions: You can use the probability fraction directly in your calculation without converting to decimals first
- Show your working: Always write down the formula and substitute your values clearly
- Units matter: If the question asks for "times" or "occurrences", make sure your answer reflects this
- Check reasonableness: Your expected frequency should make sense - it can't be more than the total number of trials!
Remember!
- Expected frequency = probability × number of trials
- It predicts what should happen, not what will definitely happen
- Always round your final answer to a whole number
- Check that your probability calculation is correct first
- The expected frequency cannot exceed the total number of trials