## Sample size, the Margin of Error and the Coefficient of Variation

### by Robert M. Lynch and Brian Kim

**Abstract:**
In introductory statistics, students are taught to determine the sample size
required for a specified Margin of Error (ME) with a known estimated standard deviation
for a population. Students are frequently challenged to identify a ME associated with the
mean. They are more comfortable with identifying a ME for a sample proportion and
frequently respond with 3 percent or 4 percent as these are common values used by the
pollsters in election coverage and other polls.
Applying the same approach to mean estimation, students become comfortable with
estimates that are within a specified percent of the mean. For example, if it is believed a
population mean is near 500, a 3 percent margin of error suggests a ME equal to 15 units
and a 4 percent ME suggests an error of 20 units. Once the ME is established, the sample
size (N) that would yield such an error can be determined.
A relationship exits between the ME when calculated as a percent of the mean, the
Coefficient of Variation (CV) and the sample size. This paper describes the relationship,
provides the algebraic equivalencies to the common sample size formula and presents
several illustrations. It also identifies several findings.
**Key Words: **
size, Margin of Error, Coefficient of Variation

**Authors:**

Robert Lynch, , robert.lynch@unco.edu

Brian Kim, mkim2@ilstu.edu

**Editor:**
Graf, R.G.
,rgraf@sunstroke.sdsu.edu

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