The following two-way table represents data from a survey asking students whether they have visited Alaska, Hawaii, or both.
\begin{tabular}{|l|l|l|l|}
\hline & Alaska & Not Alaska & Total \\
\hline Hawaii & 6 & 15 & 21 \\
\hline Not Hawaii & 8 & 21 & 29 \\
\hline Total & 14 & 36 & 50 \\
\hline
\end{tabular}
What is the relative frequency for students who have been to Alaska?
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What is the relative frequency for students who have been to Hawaii but not Alaska?
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What is the relative frequency for students who have not been to Alaska or Hawaii?
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Answer (2)
Calculate the relative frequency for students who have been to Alaska: 50 14 = 0.28 .
Calculate the relative frequency for students who have been to Hawaii but not Alaska: 50 15 = 0.30 .
Calculate the relative frequency for students who have not been to Alaska or Hawaii: 50 21 = 0.42 .
The relative frequencies are: Alaska (0.28), Hawaii but not Alaska (0.30), Neither (0.42).
Explanation
Understand the problem and provided data We are given a two-way table that summarizes survey data about students' visits to Alaska and Hawaii. The table provides counts for students who have visited Alaska, Hawaii, both, or neither. Our goal is to calculate three relative frequencies based on this data.
Define relative frequency The relative frequency is calculated by dividing the number of students in a specific category by the total number of students surveyed. In this case, the total number of students is 50.
Calculate the relative frequency for students who have been to Alaska To find the relative frequency for students who have been to Alaska, we divide the number of students who have been to Alaska by the total number of students. From the table, we see that 14 students have been to Alaska. Therefore, the relative frequency is: 50 14 = 25 7 = 0.28
Calculate the relative frequency for students who have been to Hawaii but not Alaska To find the relative frequency for students who have been to Hawaii but not Alaska, we divide the number of students who have been to Hawaii but not Alaska by the total number of students. From the table, we see that 15 students have been to Hawaii but not Alaska. Therefore, the relative frequency is: 50 15 = 10 3 = 0.30
Calculate the relative frequency for students who have not been to Alaska or Hawaii To find the relative frequency for students who have not been to Alaska or Hawaii, we divide the number of students who have not been to Alaska or Hawaii by the total number of students. From the table, we see that 21 students have not been to Alaska or Hawaii. Therefore, the relative frequency is: 50 21 = 0.42
State the final answer The relative frequency for students who have been to Alaska is 50 14 = 0.28 . The relative frequency for students who have been to Hawaii but not Alaska is 50 15 = 0.30 . The relative frequency for students who have not been to Alaska or Hawaii is 50 21 = 0.42 .
Examples
Understanding relative frequencies can help in various real-world scenarios. For instance, if a company is deciding whether to open a new branch in Alaska or Hawaii, they might survey potential customers to see how many have visited each state. The relative frequencies calculated from the survey data can help the company make an informed decision about where to invest.
The relative frequency for students who have been to Alaska is 0.28, for those who have been to Hawaii but not Alaska is 0.30, and for those who have not been to either Alaska or Hawaii is 0.42.
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