person on the school roster to determine the average height of the boys in the school. – Calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment. – Observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses. – Sending a confidential email survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town. – Taking a poll in the lunchroom (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch.
Which sample fairly represents the population? Select two options. – Measuring the height of every fiftieth person on the school roster to determine the average height of the boys in the school. – Calling every third person on the soccer team’s roster to determine how many of the team members have completed their fundraising assignment. – Observing every person walking down Main Street at 5 p.m. one evening to determine the percentage of people who wear glasses. – Sending a confidential email survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town. – Taking a poll in the lunchroom (where all students currently have to eat lunch) to determine the number of students who want to be able to leave campus during lunch.
The Correct Answer and Explanation is:
Correct Answers:
- Measuring the height of every fiftieth person on the school roster to determine the average height of the boys in the school.
- Sending a confidential email survey to every one-hundredth parent in the school district to determine the overall satisfaction of the residents of the town.
Explanation
In statistics, a sample should fairly represent the population to produce reliable and generalizable results. A fair sample is typically random, covers a broad portion of the population, and avoids bias.
The first correct choice — Measuring the height of every fiftieth person on the school roster — uses systematic sampling. This method is valid as long as the list is randomly ordered or not arranged in a way that introduces a pattern (e.g., by height, grade level, etc.). If the sample includes only boys (as the goal is to determine the average height of boys), and the roster represents the full student body fairly, this sample would provide an accurate average height of male students.
The second correct choice — Sending a confidential email survey to every one-hundredth parent in the school district — also uses systematic sampling. This is a strong method for gauging overall satisfaction of residents if all parents are part of the town population and are randomly distributed across the district. Email surveys are confidential and can reduce response bias, while every one-hundredth parent ensures a broad coverage across the town, helping to produce reliable results.
The other options are flawed:
- Calling every third person on the soccer team targets only a specific group (soccer team members), which does not generalize to the whole student body or school.
- Observing people on Main Street at 5 p.m. introduces time and location bias — it only captures those out at that time and place.
- Polling in the lunchroom may miss students who skip lunch, are absent, or are in special programs, thus not representing all students.
Fair sampling must be as inclusive and random as possible to reflect the true characteristics of the population.
