AQA A Level Maths: Statistics复习笔记5.3.1 Sample Mean Distribution

Sample Mean Distribution

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

5-3-1-sample-means-diagram-1

Worked Example

5-3-1-sample-means-we-1

Exam Tip

  • Look carefully at the distribution given to determine whether the variance or the standard deviation has been given.

 

 

 

 

 

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