Check it out! 1.5.1: Estimating Sample Proportions http://www.walch.com/wu/00113 1.5.1: Estimating Sample Proportions

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

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

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

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

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 ≈ 0.64801 Simplify. 1.5.1: Estimating Sample Proportions

To convert this decimal to a percent, multiply by 100. 0.64801 • 100 = 64.801 The graduation rate for the class of 2012 is approximately 65%. 1.5.1: Estimating Sample Proportions

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

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 ≈ 0.68966 Simplify. 1.5.1: Estimating Sample Proportions

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

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

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 ≈ 0.60401 Simplify. 1.5.1: Estimating Sample Proportions

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

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 + 2011 graduates + 2010 graduates 1.5.1: Estimating Sample Proportions

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

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 2012 + number in class of 2011 + 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

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 ≈ 0.64658 Simplify. Convert this decimal to a percent. 0.64658 • 100 = 64.658 The high school’s graduation rate over the three given years is approximately 65%. 1.5.1: Estimating Sample Proportions

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