Purpose: The following article illustrates how different tools and features can be used to understand and interpret normal distributions in real contexts.
How to Use: Below are four examples using our rollercoaster dataset. Use the examples to get ideas and tips for using authentic datasets to teach and reinforce concepts about normal distribution. Each example includes a captioned screenshot.
Example One: Dot Plot with Multiple Standard Deviations, Dividers, and Percentage
The example below demonstrates how dividers and standard deviations help calculate the percentage of data points within a specific range. This aids students in assessing if a distribution is roughly normal, bringing the Empirical Rule to life through the context of the datasets that they are working with.
Example Two: Assessing Normality Using the Empirical Rule and Standardized Distribution
In example two, the distribution has been standardized by converting the data values to Z-scores. Applying the Empirical Rule again, students can investigate the distance of different data points in Standard Deviation units and assess if a given value is unusual compared to the rest of the group.
Example Three: Standard Error of the Mean Sample
Our final example shows the mean and standard deviation of a sample, along with the Standard Error of the Mean (SEM). Students use the SEM as a metric to estimate the distance of the sample mean from the true population mean.