1. Check it out! 1.5.1: Estimating Sample Proportions
1.5.1: Estimating Sample Proportions

2. A local high school records data about each graduating class
A local high school records data about each graduating class. The following table shows graduation and enrollment numbers for members of three given graduation years. The table includes the number of students who graduated in each given class, the number of students in each class who did not graduate but were still enrolled at the end of that year, and the number of students who did not graduate and were no longer enrolled at the end of that year.
Class
Graduated
Still enrolled
No longer enrolled
2012
1,042
345
221
2011
1,120
306
198
2010
1,025
450
222
Common Core Georgia Performance Standards: MCC9–12.S.IC.4★
1.5.1: Estimating Sample Proportions

3. What is the high school’s graduation rate over the three given years?
What is the graduation rate for each class: 2012, 2011, and 2010? Round your answer to the nearest percent.
What is the high school’s graduation rate over the three given years?
Which class best represents the overall graduation rate? Explain your reasoning.
1.5.1: Estimating Sample Proportions

4. What is the graduation rate for each class: 2012, 2011, and 2010
What is the graduation rate for each class: 2012, 2011, and 2010? Round your answer to the nearest percent.
To find the graduation rate for each class, first calculate the total number of students in the class.
The table indicates three possible categories for students in each graduating class: the number of students who graduated that year, the number who did not graduate but were still enrolled at the end of that year, and the number who did not graduate and were no longer enrolled at the end of that year.
To find the graduation rate for a given class, divide the number of students who graduated by the total number of students in the class.
1.5.1: Estimating Sample Proportions

5. total = graduated + still enrolled + no longer enrolled
Class of 2012
To find the total number of students in the class, find the sum of the three categories:
total = graduated + still enrolled + no longer enrolled
The class of 2012 had 1,608 students.
graduated + still enrolled + no longer enrolled
Total number of students
(1042) + (345) + (221)
Substitute values from the table.
1608
Simplify.
1.5.1: Estimating Sample Proportions

6. Substitute known values.
Calculate the graduation rate for the class of 2012 by dividing the number of graduates (1,042) by the total number of students in the class. Formula:
Substitute known values.
graduation rate ≈ Simplify.
1.5.1: Estimating Sample Proportions

7. To convert this decimal to a percent, multiply by 100.
• 100 =
The graduation rate for the class of 2012 is approximately 65%.
1.5.1: Estimating Sample Proportions

8. total = graduated + still enrolled + no longer enrolled
Class of 2011
Find the total number of students in the class:
total = graduated + still enrolled + no longer enrolled
The class of 2011 had 1,624 students.
graduated + still enrolled + no longer enrolled
Total number of students
(1120) + (306) + (198)
Substitute values from the table.
1642
Simplify.
1.5.1: Estimating Sample Proportions

9. Substitute known values.
Calculate the graduation rate by dividing the number of graduates (1,120) by the total number of students in the class. Formula:
Substitute known values.
graduation rate ≈
Simplify.
1.5.1: Estimating Sample Proportions

10. Convert this decimal to a percent. 0.68966 • 100 = 68.966
The graduation rate for the class of 2011 is approximately 69%.
1.5.1: Estimating Sample Proportions

11. total = graduated + still enrolled + no longer enrolled
Class of 2010
Find the total number of students in the class:
total = graduated + still enrolled + no longer enrolled
The class of 2010 had 1,697 students.
graduated + still enrolled + no longer enrolled
Total number of students
(1025) + (450) + (222)
Substitute values from the table.
1697
Simplify.
1.5.1: Estimating Sample Proportions

12. Substitute known values. graduation rate ≈ 0.60401 Simplify.
Calculate the graduation rate by dividing the number of graduates (1,120) by the total number of students in the class. Formula:
Substitute known values.
graduation rate ≈ Simplify.
1.5.1: Estimating Sample Proportions

13. Convert this decimal to a percent. 0.60401 • 100 = 60.401
The graduation rate for the class of 2010 is approximately 60%.
1.5.1: Estimating Sample Proportions

14. What is the high school’s graduation rate over the three given years?
To find the graduation rate for the entire three years, start by finding the total number of graduates for the three years:
total number of graduates = 2012 graduates graduates graduates
1.5.1: Estimating Sample Proportions

15. Total number of graduates
(1042) + (1120) + (1025)
Substitute values from the table.
3187
Simplify.
The total number of students for all three given years is 3,187.
1.5.1: Estimating Sample Proportions

16. Total number of students
Find the total number of students in all three classes by summing the totals found for each class in problem 1.
number in class of number in class of number in class of 2010
Total number of students
(1608) + (1624) + (1697)
Substitute values found in problem 1.
4929
Simplify.
The total number of students for all three given years is 4,929 students.
1.5.1: Estimating Sample Proportions

17. Substitute known values. graduation rate ≈ 0.64658 Simplify.
As in problem 1, divide the number of graduates by the total number of students.
Substitute known values.
graduation rate ≈ Simplify.
Convert this decimal to a percent.
• 100 =
The high school’s graduation rate over the three given years is approximately 65%.
1.5.1: Estimating Sample Proportions

18. The class of 2012 had a graduation rate of 65%.
Which class best represents the overall graduation rate? Explain your reasoning.
Compare the graduation rates for each class with the overall graduation rate for the three given years.
The class of 2012 had a graduation rate of 65%.
The class of 2011 had a graduation rate of 69%.
The class of 2010 had a graduation rate of 60%.
The overall graduation rate for the three given years is 65%.
The class whose graduation rate most closely matches the overall rate of 65% is the class of 2012; therefore, the class of 2012 best represents the overall graduation rate.
Connection to the Lesson
Students will continue to work with data to investigate sample populations.
Students will also relate samples to populations.
1.5.1: Estimating Sample Proportions