Biased Sample — Definition, Formula & Examples
A biased sample is a sample collected in a way that makes some members of the population more likely to be included than others. Because certain groups are over- or under-represented, conclusions drawn from a biased sample can be misleading.
A sample is biased when the method of selection systematically favors certain outcomes, causing the sample statistics to differ from the corresponding population parameters in a predictable direction.
How It Works
Bias creeps in whenever the sampling method gives an unfair advantage to part of the population. For example, surveying people only at a shopping mall excludes those who rarely shop there. To check for bias, ask: "Could any group in the population have had zero or very low chance of being selected?" If yes, the sample is likely biased. The fix is usually to use a random sampling method so every member of the population has an equal chance of being chosen.
Example
Problem: A school has 800 students. The principal wants to know the average number of hours students sleep per night. She surveys the 40 students in the before-school tutoring program (which starts at 6:45 AM). Is this sample biased?
Identify the population: The population is all 800 students in the school.
Examine the sampling method: Only students who attend early-morning tutoring were surveyed. These students wake up earlier than most, so they may also go to bed earlier or get less sleep than the typical student.
Determine if bias exists: Students who do not attend the tutoring program had no chance of being selected. Their sleep habits could differ significantly, so this sample systematically excludes a large portion of the population.
Answer: Yes, the sample is biased. It only includes early-morning tutoring students, whose sleep patterns likely do not represent the entire school. A random sample of 40 students from all 800 would give more reliable results.
Why It Matters
In science fair projects, opinion polls, and medical studies, biased samples lead to wrong conclusions. Learning to spot bias now prepares you for evaluating real-world data in courses like AP Statistics and in careers such as market research, public health, and data science.
Common Mistakes
Mistake: Thinking a large sample automatically removes bias.
Correction: Sample size and bias are separate issues. A survey of 10,000 people can still be biased if it only reaches one type of person. You need a random or representative selection method, not just more responses.