Education Technology

Center and Spread

Activity Overview

Students will recognize that the mean and standard deviation (SD) and the median and interquartile range (IQR) are two ways to measure center and spread.

Objectives

  • Students will recognize that the mean and standard deviation (SD) and the median and interquartile range (IQR) are two ways to measure center and spread.
  • Students will recognize that in a skewed distribution the mean is pulled in the direction of the tail, and the standard deviation is increased; in a distribution with an outlier, the mean is pulled in the direction of the outlier, and the standard deviation is increased.
  • Students will be able to illustrate that the median and IQR are resistant to skewness/outliers while the mean and standard deviation are not.
  • Students will recognize that the median and IQR are preferred when a distribution is skewed while either mean and SD or median/IQR are acceptable for approximately symmetric distributions.

Vocabulary

  • Bimodal or unimodal
  • Interquartile range
  • Mean, median, and standard deviation
  • Outlier
  • Resistant
  • Akewed or symmetric distribution

About the Lesson

This lesson involves moving points on dotplots. Students will:

  • change the shape of the distribution and notice the effect on the mean and median and on the standard deviation and IQR.
  • drag points to compare the effect of outliers on the mean/standard deviation and median/IQR.
  • make and justify a conjecture about which measures are preferred based on the shape of the distribution.