# Sample Surveys

## 10. Calculating Estimates

Once the data are collected and survey sampling weights are computed, one uses the data and weights to estimate characteristics of the population. If the survey data are collected based on a simple random sample and there are no complications, then reporting the average of the sample values produces a statistically unbiased estimate of the population average.

Standard deviation (SD) is used to measure the variability (or dispersion or spread) of observations while the standard error (SE) is the standard deviation of a statistic.

When using sample means as a method of estimating the population mean, the standard error of the mean is the standard deviation of the sample means calculated over all possible samples of a given size drawn from the population.  It is frequently estimated by taking the standard deviation of a sample and dividing by the square root of the number of observations in the sample.

The unbiasedness of the sample mean in this case is a property of the sampling design and the estimator (procedure used to turn the data values into an estimate). It means that when estimates from every possible sample selected using the specified sample design are averaged, the average is equal to the population parameter that is estimated by the estimator.  This is illustrated in Figure 2.

### Figure 2 