Education Technology

# Activities

Aust Senior

50 Minutes

• ##### Device
• TI-84 Plus CE
• TI-83/TI-84 Plus Family

## How Long - Sampling Distributions

#### Activity Overview

Suppose two points are randomly placed inside a 1cm x 1cm square, on average, how far apart would you expect the points to be? A simulation is set up to help answer the question. Multiple samples can easily be generated using user defined sizes. The mean of each sample is automatically recorded and graphed to form a sampling distribution. Students gain an understanding of the relationship between sample size and the standard deviation of the corresponding sampling distribution.

#### Vocabulary

• Random,
• Mean,
• Sampling and Sampling Distribution,
• Standard deviation and Variance

#### About the Lesson

A program is used to generate a graphical representation of the problem: Two points are randomly placed inside a 1cm x 1cm square, how far apart would you expect the points to be? The program can also generate single samples of a nominated size or multiple samples and the corresponding sampling distribution for the mean. The visual nature of the problem combined with the questions and simulations provides for an intuitive understanding of the relationship between the size of each sample and the standard deviation of the sampling distribution. The precise relationship is not used, instead the activity focuses on the concept, including an informal approach to the central limit theorem.