Math Example--Measures of Central Tendency--Sample Mean--Example 4

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the sample mean for a group of 30 macaws. The image shows a table with the wingspans of these macaws and the formula for calculating the sample mean. The population of adult macaws has an average wingspan of 48 inches with a standard deviation of 6. The sample mean is computed by summing all the wingspans (1432.28 inches) and dividing by the number of macaws (30), yielding a sample mean of 47.74 inches.

Measures of central tendency are fundamental in statistics, providing a way to describe the typical or central value in a dataset. This collection of examples aids in teaching this topic by presenting various scenarios where the sample mean is calculated and compared to the known population mean. By using different populations (trout in previous examples, macaws in this one), students can see how sample means may vary but generally approximate the population mean across different contexts.

Offering multiple worked-out examples is crucial for students to thoroughly understand the concept of sample mean. Each example reinforces the calculation process while demonstrating how sample means can differ from the population mean and from other samples. This repetition helps students build confidence in their ability to calculate and interpret sample means across diverse situations and recognize the applicability of this concept to various real-world scenarios.

Teacher's Script: Let's examine our fourth example of calculating a sample mean. This time, we're looking at the wingspans of 30 macaws. How is this example similar to our previous ones? How is it different? Let's calculate the sample mean together. How does it compare to the population mean? What does this tell us about the usefulness of sample means across different types of data?

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