ExpertMedium3 marksExtended Response
AQA GCSE · Question 11 · Data Collection and Sampling Methods
Tate is going to play a game at a fair. The game has a 5 by 5 grid and behind some of the 25 squares are prizes.
Tate decides he wants to pick one square at random.
Describe how he could use cards numbered 1 to 25 to do this.
Tate is going to play a game at a fair. The game has a 5 by 5 grid and behind some of the 25 squares are prizes.
Tate decides he wants to pick one square at random.
Describe how he could use cards numbered 1 to 25 to do this.
How to approach this question
The goal is to select one number from 1 to 25 in a way that every number has an equal chance of being chosen. Think of a lottery or a raffle. What steps would you take with the numbered cards to ensure the selection is fair and random?
Full Answer
1. Place the 25 cards into a bag or hat.
2. Shake the bag thoroughly to mix the cards.
3. Without looking, draw one card out of the bag. The number on the card corresponds to the square he should pick.
To make a random selection, every item in the population (in this case, the 25 squares) must have an equal chance of being chosen. Using cards numbered 1 to 25 is a classic method for simple random sampling. The process is:
1. **Place all cards in a container:** Put the 25 cards into a bag, box, or hat. This ensures all possible choices are present.
2. **Mix them thoroughly:** Shake the bag or shuffle the cards well. This step is crucial to eliminate any bias from the order in which the cards were placed in the bag.
3. **Select one card without looking:** Reach into the bag without looking and draw out a single card. This ensures the selection is blind and not influenced by the person picking.
The number on the chosen card then corresponds to the square Tate will pick on the grid (assuming the squares are also numbered 1 to 25).
Common mistakes
✗ Missing a key step, such as mixing the cards. Just putting them in a bag and picking is not enough to guarantee randomness if they are not mixed.
✗ Describing a non-random method, e.g., "spread the cards on a table and pick one". This could introduce bias as some cards might be easier to pick.
Practice the full AQA GCSE Statistics Foundation Tier Paper 1
47 questions · hints · full answers · grading
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