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?

Answer 1

Answer: The middle school has: 160 sixth graders, 180 seventh graders and and 140 eighth graders.

if in the sample of seventh graders were, chosen 9 of them, this is a 9/180= 0.05, or 5% of the total sample of seventh graders.

then, we also need to select a 5% of the total population of sixth graders for the survey, this is 0,05*160= 8, but remember that you need to select this 8 students at random.

Answer 2

You need to look at this as a proportion and ratio.

If $\frac{9}{180}$ seventh graders were chosen, that is $\frac{1}{20}$ of them.

You need to find $\frac{1}{20}$ of the sixth graders to remain constant.

$\frac{1}{20}$ of 160 = 8 students.