ExpertEasy1 markMultiple Choice
AQA GCSE · Question 03 · Data Collection and Sampling Methods
Olivia wants to obtain a systematic sample of size 40 from a population of 2000 competitors in a race. She numbers the competitors from 1 to 2000 and uses, as a starting point, competitor number 11. Circle the correct competitor number of the next person in her sample.
Olivia wants to obtain a systematic sample of size 40 from a population of 2000 competitors in a race. She numbers the competitors from 1 to 2000 and uses, as a starting point, competitor number 11. Circle the correct competitor number of the next person in her sample.
Answer options:
A.
12
B.
21
C.
51
D.
61
How to approach this question
First, calculate the sampling interval (k) by dividing the population size by the desired sample size. Then, add this interval to the starting number to find the next person in the sample. \n1. Population size (N) = 2000. \n2. Sample size (n) = 40. \n3. Calculate interval: k = N / n. \n4. Next person = Starting number + k.
Full Answer
D.61✓ Correct
The correct answer is 61.
Systematic sampling involves selecting items from an ordered population using a fixed, periodic interval. \n1. Calculate the sampling interval (k): k = Population size / Sample size = 2000 / 40 = 50. \n2. The starting point is given as competitor number 11. \n3. To find the next person in the sample, add the interval to the starting point: Next number = 11 + 50 = 61. The sample would consist of competitors 11, 61, 111, 161, and so on.
Common mistakes
✗ Using the sample size (40) as the interval.\n✗ Simply adding 10 or 1 to the starting number.\n✗ Incorrectly calculating the interval (e.g., 40 / 2000).
Practice the full AQA GCSE Statistics Higher Tier Paper 2
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