Math Example--Measures of Central Tendency--Sample Mean--Example 1

Topic

Measures of Central Tendency

Description

This example demonstrates the calculation of the sample mean for a group of 30 trout. The image displays a table showing the lengths of these trout, along with the formula for calculating 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 calculated by summing all the lengths (472.22 inches) and dividing by the number of trout (30), resulting in a sample mean of 15.74 inches.

The topic of measures of central tendency is crucial in statistics, providing a way to describe the typical or central value in a dataset. This collection of examples helps teach this topic by presenting various scenarios where the sample mean is calculated and compared to the known population mean. By using different sample sizes and populations (trout, macaws, elephants, sequoia trees), students can see how sample means may vary but generally approximate the population mean.

Presenting multiple worked-out examples is essential for students to fully grasp the concept of sample mean. Each example reinforces the calculation process while showcasing how sample means can differ from the population mean. This repetition helps students develop confidence in their ability to calculate and interpret sample means across diverse situations.

Teacher's Script: Now, let's look at our first example of calculating a sample mean. We have data on the lengths of 30 trout. Remember, the sample mean gives us an estimate of the population mean. Can you tell me how we calculate it? That's right, we sum up all the lengths and divide by the number of trout. Let's do this calculation together and compare our result to the known population mean. What do you notice about the difference between our sample mean and the population mean?

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.