Question

A middle school has

220 students in grade 6;
170 students in grade 7; and
100 students in grade 8.

The media specialist wants to know which books are the most popular among the students in her school. Since she cannot ask all the students, she will survey a group of them.

Which sample can best help the media specialist draw conclusions about the preferences of all the students in the school?

A. 45 sixth graders, 35 seventh graders, 20 eighth graders

B. 20 sixth graders, 35 seventh graders, 45 eighth graders

C. 45 sixth graders, 45 seventh graders, 45 eighth graders

D. 20 sixth graders, 20 seventh graders, 20 eighth graders​

Answer 1

Option A.

Explanation:

We know that we have:

220 students in grade 6.

170 students in grade 7.

100 students in grade 8.

Now we want to make a sample, to have the sample in the most representative way, so we should select the same percentage of students for each grade.

Let's analyze option A (this is the one that makes sense because has the larger number for 6th grade, then 7th grade and last for 8th grade)

Here we need to look at the quotient between the number of students selected for each grade, and the total number of students in the grade:

for 6th grade:

45/220 = 0.2

for 7th grade:

35/170 = 0.21

for 8th grade:

20/100 = 0.2

In the 3 cases we can see that we have almost the same ratio, which means that for the sample we selected around the 20% of each grade.

This is the most representative way of sampling in this case, then the correct option is A.