Math Example--Measures of Central Tendency--Sample Mean--Example 2

Topic

Measures of Central Tendency

Description

This example presents another calculation of the sample mean for a group of 30 trout. The image shows a table with the lengths of these trout and the formula for the sample mean. The population of adult trout has a mean length of 15 inches with a standard deviation of 2. The sample mean is computed by adding all the lengths (436.73 inches) and dividing by the number of trout (30), yielding a sample mean of 14.56 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 samples from the same population (trout) and other populations (macaws, elephants, sequoia trees), students can observe how sample means may fluctuate but generally approximate the population mean.

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.

Teacher's Script: Let's examine our second example of calculating a sample mean. We have another set of data on the lengths of 30 trout. Remember, even though we're looking at the same type of fish, our sample will likely be different from the first one. Can you explain why? Now, let's calculate this new sample mean together. How does it compare to our first sample mean and the population mean? What might explain these differences?

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.