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GB-30-01-001 · Stratified sampling

A school has the following numbers of students.

Year 9Year 10Year 11
1005244
A stratified sample of 49 students is needed. Work out how many Year 10 students should be selected.

Tagged / Stratified Sampling (Proportion Fractions) Booklet p. 22
Method
1) Define x
2) Match population and sample fractions
3) Cross multiply
4) Solve
Worked Example (GB-30-01-001)
1)
Let x be the number of Year 10 students in the sample. Total students: 100+52+44=196100+52+44=196.
2)
Keep the same group fraction in the population and sample: 52196=x49\frac{52}{196}=\frac{x}{49}.
3)
Cross multiply: 196x=52×49=2548196x=52\times49=2548.
4)
Divide: x=2548196=13x=\frac{2548}{196}=13. Select 1313 Year 10 students.
Ans = 13