A researcher wants to select a sample of 50 students from four local private high schools by performing stratified sampling. The enrollments are shown in the table. How many students at each school should be included in the study?
A= 800
B= 100
C=60
D=40
The study should include 40 students from school A,
5 students from school B,
3 students from school C, and
2 students from school D.
I got these answers by dividing 800/4 =200/5 to get answer a 40.
Then dividing 100/4 =25/5 to get answer b 5. Then dividing 60/4 =15/5 to get answer c 3. Then dividing 40/4 =10/5 to get answer d 2.
Well, if your math checks out, then it seems like you've cracked the equation! So, you should include 40 students from school A, 5 students from school B, 3 students from school C, and 2 students from school D. Good job, math whiz!
Yes, that is correct. To perform stratified sampling, you need to divide the total number of students in each school by the total number of students in all the schools combined, and then multiply that ratio by the desired total sample size.
For School A: (800/1000) * 50 = 40 students
For School B: (100/1000) * 50 = 5 students
For School C: (60/1000) * 50 = 3 students
For School D: (40/1000) * 50 = 2 students
So, the study should include 40 students from School A, 5 students from School B, 3 students from School C, and 2 students from School D.
To perform stratified sampling, you need to choose a proportionate number of students from each school based on their enrollment size.
First, calculate the total enrollment size by summing up the enrollments of all the schools:
Total enrollment size = A + B + C + D
Total enrollment size = 800 + 100 + 60 + 40 = 1000
Next, calculate the proportion of each school's enrollment out of the total enrollment size:
Proportion of school A = A / Total enrollment size
Proportion of school B = B / Total enrollment size
Proportion of school C = C / Total enrollment size
Proportion of school D = D / Total enrollment size
Proportion of school A = 800 / 1000 = 0.8
Proportion of school B = 100 / 1000 = 0.1
Proportion of school C = 60 / 1000 = 0.06
Proportion of school D = 40 / 1000 = 0.04
Finally, multiply the desired sample size (50) by each school's proportion to determine how many students should be included from each school:
Number of students from school A = Proportion of school A x Desired sample size
Number of students from school B = Proportion of school B x Desired sample size
Number of students from school C = Proportion of school C x Desired sample size
Number of students from school D = Proportion of school D x Desired sample size
Number of students from school A = 0.8 x 50 = 40
Number of students from school B = 0.1 x 50 = 5
Number of students from school C = 0.06 x 50 = 3
Number of students from school D = 0.04 x 50 = 2
Therefore, the study should include 40 students from school A, 5 students from school B, 3 students from school C, and 2 students from school D.