Math Example--Measures of Central Tendency--Weighted Mean--Example 9

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of a weighted mean in the context of probability, specifically finding the average sum when rolling two fair dice. The image displays a grid showing all possible outcomes of rolling two dice, with sums ranging from 2 to 12. The frequencies of each sum are highlighted in red, serving as the weights in the weighted mean calculation. The weighted mean is computed using the formula: (2 * 1 + 3 * 2 + 4 * 3 + 5 * 4 + 6 * 5 + 7 * 6 + 8 * 5 + 9 * 4 + 10 * 3 + 11 * 2 + 12 * 1) / 36, resulting in an average sum of 7.

Weighted mean is an essential concept in measures of central tendency, allowing for the consideration of the relative frequency or probability of each outcome. This collection of examples helps teach this topic by providing scenarios that bridge mathematics and probability, such as calculating the average sum of rolling dice. It enables students to understand the application of the weighted mean formula in contexts involving chance and expected values.

Presenting multiple worked-out examples, particularly those connecting to probability and games of chance, is crucial for students to fully comprehend the concept of weighted mean. By observing the formula applied to diverse situations, students can develop a deeper understanding of how weights influence the final average and how to interpret the results in scenarios involving probability and expected outcomes.

Teacher's Script: Let's explore this fascinating example of using weighted mean in a probability context. How does this differ from our previous examples with coins or kettlebells? Can you think of other games or situations where we might use weighted means to calculate expected outcomes?

For a complete collection of math examples related to Measures of Central Tendency click on this link: Math Examples: Measures of Central Tendency: Weighted Mean Collection.