Statistics: Trend or Noise?

Objectives

• Students will recognize that samples from a population typically have smaller variability than the population.
• Students will recognize that many reported patterns are really nothing but random noise and not patterns at all.
• Students will recognize that small samples might have more variability than large samples.

Vocabulary

• distribution
• boxplots
• interquartile range (IQR)
• mean
• median
• sample

About the Lesson

This lesson involves investigating aspects of statistical information reported in the media or other venues, aspects that are often misunderstood by those unfamiliar with sampling.
As a result, students will:

• Look at a randomly-generated distribution of student achievement scores for a whole grade and for the individual classes in that grade
• Analyze boxplots of the data and observe the variation among the classes, identifying a class that seems to have higher scores.
• Analyze the distribution of the mean scores for each class in the grade and relate it to the distribution of the scores for the entire grade.
• Choose one of the teachers' classes and examine the scores for that teacher across consecutive years, looking for trends or seemingly large changes.