Question

a population of middle school students contains 160 sixth - graders, 180 seventh - graders, and 140 eighth - graders. nine seventh - graders were part of a random sample of the population chosen to participate in a survey. for the sample to accurately represent the population, about how many sixth - graders should be chosen?
7
8
14
16

Explanation:

Step1: Calculate the sampling ratio for seventh - graders

The ratio of seventh - graders in the sample to the total number of seventh - graders is $\frac{9}{180}=\frac{1}{20}$.

Step2: Use the same ratio to find the number of sixth - graders in the sample

Let $x$ be the number of sixth - graders in the sample. We set up a proportion using the same sampling ratio. So $\frac{x}{160}=\frac{1}{20}$. Cross - multiply gives $x=\frac{160}{20}=8$.

Answer:

B. 8