Video: Solving Word Problems Involving a Stratified Sample

A school has 500 students; 320 of them are boys. To select students for a survey, a stratified sample of 25 students will be taken. How many boys and how many girls will be selected by the sample.

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Video Transcript

A school has 500 students. 320 of them are boys. To select students for a survey, a stratified sample of 25 students will be taken. How many boys and how many girls will be selected by the sample?

So out of all of the students, we know how many of them are boys. Out of the 500 students in the school, 320 of them are boys. So if the stratified sample is 25 students, we need to take this fraction, multiply it by 25, or 25 over one.

25 can go into 500 20 times. And 320 divided by 20 is 16. So we would expect 16 boys to be selected by the sample. So if there are 25 students in the sample, we can take 25 minus 16 to find the number of girls, which will be 9. So there are 16 boys and 9 girls in the sample.

Another way that we could have found the number of girls would be to use the fact that there are 320 boys in the school. So how many would be left for the girls? Well, subtract that from 500 and we get 180. So 180 out of the 500 students will be girls. So you would take this, multiply it by 25, or 25 over one.

25 simplifies with 500 because 25 goes into 25 once. And 25 goes into 500 20 times. And then 180 divided by 20 would give us an answer of nine. So once again, there are 16 boys and nine girls in the sample.

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