Lesson 6: Choose Appropriate Statistical Measures

Property

The shape of the distribution completely changes the relationship between the Mean and the Median:

• Symmetric: Mean $\approx$ Median. Both sit perfectly in the center.
• Skewed Right: Mean $>$ Median. Extreme high values pull the mean to the right.
• Skewed Left: Mean $<$ Median. Extreme low values pull the mean to the left.

Examples

• Skewed Right Example: In a neighborhood, most homes cost $200,000 (Median), but one mansion costs$2,000,000. This massive outlier pulls the average (Mean) up to $450,000. The Median ($200k) is a much more honest representation of the "typical" home.
• Skewed Left Example: Most students score an 85 or 90 on a test (Median), but two students fall asleep and score a 10. These low scores pull the class average (Mean) down to a 72. The Median (85) better represents how the typical student performed.

Explanation

Property

To summarize a data set, follow this process:

1. Analyze Shape: Examine a data display (like a dot plot) to determine if the distribution is symmetric or non-symmetric.
2. Choose Measures: Select the mean and MAD for symmetric data, or the median and IQR for non-symmetric data.
3. Calculate: Compute the values for the chosen measures of center and variability.

Examples