What is the distribution of the sample means?
- For any given population it can often be difficult or impractical to find the true value of the population mean, µ
- The population could be too large to collect data using a census or
- Collecting the data could compromise the individual data values and therefore taking a census could destroy the population
- Instead, the population mean can be estimated by taking the mean from a sample from within the population
- The standard deviation of the distribution of the sample means depends on the sample size, n
- It is inversely proportional to the square root of the sample size
- This means that the greater the sample size, the smaller the value of the standard deviation and the narrower the distribution of the sample means
- Look carefully at the distribution given to determine whether the variance or the standard deviation has been given.