Rangeland Ecology & Management

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Sample Mean

The sample mean (x-bar) is the average of a set of values that are sampled from a population. Because vegetation attributes usually exhibit a normal distribution, a greater proportion of the data will lie close to the mean. The sample mean is computed by adding all values in a sample data set and dividing by the number of values in the data set.

x-bar = (sum of x) / n

The population mean (greek letter mu) is calculated in the same manner. However, because we usually aren't able to collect data on all members of the population, we can use the sample mean to estimate the population mean, based on the assumption that they are equal.

mu = x-bar

This relationship between the sample mean and the population mean will be valid whenever the attribute being sampled exhibits a normal distribution, and the sampling procedure is free of bias. Safeguards incorporated into the sampling process to protect against bias are discussed under Accuracy and Bias.

References and Further Reading

Bonham, C.D. 1989. Measurements for terrestrial vegetation. John Wiley Son, New York, NY. pp 52-54.

Cook, C.W., and J. Stubbendieck. (eds). 1986. Range research: Basic problems and techniques. Society for Range Management, Denver, CO. pp 217-219.