Resources

Math: Statistics and estimating

Measurement errors

Calculation of sampling error (also called standard error) is based on the standard deviation of the sample: the greater the sample standard deviation, the greater the sampling error. The sampling error is also related to the sample size. The greater your sample size, the smaller the sample error. This error cannot be avoided, only reduced by increasing the sample size.

It is possible to estimate the range of random error at a particular level of confidence. Suppose we surveyed 500 people and found that 65% of them said that vanilla is their favorite ice cream. For a sample of 500, sampling error is 4 percent. This means that we can expect our sample results to be within 4 percentage points of the actual figure for the population — in other words, as high as 69% or as low as 61%. As sample size increases, sampling error decreases. Sampling error is 10% for a sample of 100 and 3% for a sample of 1000.

When the area of the standard normal curve is divided into sections by standard error above and below the mean, the area in each section is a known quantity. The areas above and below the mean can be added together to get the probability of obtaining a value within (plus or minus) a given number of standard errors. There is a 65% chance of a value falling within one standard error of the mean, a 95% chance within two standard errors, and a 99% chance that it will be within three.

Suppose a normal distribution has a mean of 3.75 (highest point on the graph below) and a standard deviation of 0.25. Then 65% of the values will fall between 3.5 and 4.0, as shown below.

Description

**"Q&A: Measurement errors"** 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.

FORMATS AVAILABLE:

Printer-friendly web page

GRADES:

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 sampling error?" 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.

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