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Math: Statistics and estimating

A 1:

Bias is a systematic error in sample statistics that can occur from the use of poor sampling methods. Sample design results may be biased for a number of reasons, such as frame error or selection error.

The sampling frame is the list of population elements or members from which the sample is selected. Frame error results when the sampling frame does not represent a true cross-section of the target population. For example, suppose you survey your neighborhood and talk only to the people on the street. Any data collected in this manner are heavily biased because not everybody in the neighborhood had a chance to respond — what about the people who were inside at the time of the survey? Any conclusions drawn about your neighborhood using this method of sampling will not be representative of the population, i.e., the entire neighborhood.

Selection error involves a systematic bias in the manner in which respondents are selected for participation in the survey. Even if the sampling frame is defined properly to include the appropriate population members, selection error can still occur. Incomplete or improper procedures for selecting participants will lead to selection error. If a sample list was sorted by zip code and interviewers selected survey participants by contacting names in order from the beginning of the list, selection error would occur because those members of the population appearing at the end of the list (larger zip codes) would never be contacted.


A 2:

When bias occurs, the results are skewed from the normal distribution. A negatively skewed curve has a thicker tail on the side below the mean, while a positively skewed distribution has a larger tail on the side above the mean. In either case, the accuracy of the results will be compromised. Note: a skewed sample does not necessarily mean it is biased.


A 3:

The answer is no. A computer's random number generator could be programmed in such a manner as to yield a biased sample. However, for the purposes of the Amazing Space "Galaxy Hunter" online exploration, computers are considered unbiased.


"Q&A: Bias" is a series of questions and answers about statistics written for teachers and students. The questions are ones that students might ask while studying statistics. Teachers can use this Q&A to gain additional knowledge about statistics, or use it in the classroom as outlined below.

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Adaptable, at teacher's discretion
How to use in the classroom

• An engagement activity. Use selected questions to start a discussion.

• An inquiry tool. Use selected questions and answers to help students generate questions. Propose a question, such as "What is bias?" Have students read the answer to the question and write down 3–5 questions they would like answered as a result of reading the material.

• A source of information. Students can use the questions and answers as part of their research on statistics.

• A form of review. Use the questions as a review at the end of a unit on statistics.

• A follow-up. Have students read the questions and answers to gain additional information about statistics following a related activity.

• A starting point for debate. "Is a computer always unbiased, and do computers always produce random samples?" These idea are addressed in question 3.


Related materials

Online Exploration: Galaxy Hunter