Estimating means and proportions

A random sample is often selected from a population in order to estimate some particular numerical summary of it. The population characteristic of interest might be...

Although we do not know the value of the population mean or proportion, the corresponding value from a sample can be used to estimate it. Estimation will be considered in greater depth in the next chapter, but we note here that the sample mean or proportion is usually different from the target population mean or proportion.

The difference between an estimate and the value being estimated is called its sampling error.

When a population characteristic is estimated from a sample, there is usually a sampling error.

Estimating the proportion of males

The diagram below again illustrates the sampling of 15 people from a group of 56.

Click Take sample a few times and observe that the sample proportion of males varies from sample to sample. The difference between the estimate and the population proportion of males is the sampling error.

Estimating the proportion of defective boxes

The diagram below shows 120 boxes, some of which are defective.

Click Take sample a few times to select samples of 17 boxes. Observe resulting sampling errors.

Estimating a mean age

The diagram below shows the ages of 49 students attending a night-school class about local history.

Click Take sample a few times to select 10 of these students at random. Observe the variability in the sample mean age and its difference from the true mean age in the class (the sampling error).