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 damaged bags

The diagram below shows 90 bags that have been unloaded from a plane, some of which are damaged.

Click Take sample a few times to select samples of 15 bags. Observe resulting sampling errors.

Estimating the mean time to pay an invoice

The diagram below shows the time (days) between a garage sending invoices for car repairs and receiving payment, for the 80 invoices that were delivered in one week.

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