Statistical Bias and Sampling Worksheets Grade 10

1. Matiu wants to estimate the average height of all students at his school. He stands outside the gymnasium after a basketball game and asks every 5th person who leaves to measure their height. Identify the type of sampling method used, describe the potential bias, and explain how this could affect the estimate.
2. Matiu is a health researcher investigating physical activity levels among high school students in his city. He posts an online survey link on a popular social media platform and asks students to voluntarily complete it. A total of 240 students respond, and the results show that 85% of them report exercising for at least 60 minutes daily. Identify and explain the type of bias most likely present in this sampling method, and describe how this bias could affect the generalizability of Matiu's findings to all high school students in the city.
3. A local park has a rectangular garden that is 28 meters long and 14 meters wide. The garden is divided into four equal rectangular sections by two paths: one path runs parallel to the length through the middle, and the other runs parallel to the width through the middle. The paths are 2 meters wide each. Mason wants to survey park visitors about their favorite flower type. He decides to stand at the entrance of the garden and ask every 5th person who enters. Is this a biased sampling method? If so, identify the type of bias and explain why it is problematic.

…and 1 more problems

1. Mason wants to estimate the average number of hours students at his school spend on homework each week. He surveys 72 students who are members of the chess club. Identify the type of sampling bias present and explain why it is a problem.
2. Aroha wants to estimate the average height of trees in a large forest. She stands at the entrance and measures the first 75 trees she sees. Identify the sampling method used, the type of bias present, and explain why this sample may not represent the entire forest.
3. Ava is a school board member investigating whether students at her high school support a new later start time of 9:00 AM. She posts a question on the school's main social media page and asks students to comment 'yes' or 'no' with their reasons. Within 24 hours, she receives 450 responses, with 76% of them in favor of the later start time. Identify the sampling method used, name the type of bias present, and explain why this method leads to biased results.

…and 3 more problems

1. Matiu is a researcher studying the average weekly screen time of high school students in his city. He posts a link to an online survey on his social media page and asks his followers to participate. Within a week, 240 students complete the survey. The average screen time reported by these respondents is 42 hours per week. Identify and explain two distinct types of bias present in Matiu's sampling method, and discuss how each bias could affect the generalizability of his results to all high school students in the city.
2. Mere is a community health researcher studying physical activity levels among adults in her city. She posts a survey link on a popular fitness forum and receives 420 responses. Of these, 85% report exercising at least 30 minutes daily. Identify and explain the most significant type of sampling bias present in this study, and describe how it affects the generalizability of the results to all adults in the city.
3. A university is studying the average study time per week for undergraduate students. They randomly select 500 students from their enrollment database, but only 180 students respond to the survey. The respondents have an average study time of 18 hours per week, while the non-respondents are later found to average only 8 hours per week. Calculate the actual average study time for all 500 selected students, accounting for non-response bias.

…and 2 more problems