Education Technology

# Summarizing Distributions of Univariate Data

Math: Statistics: Inferential Statistics
9-12
60 Minutes
TI Connect™
TI-89 / TI-89 Titanium
This is Activity 2 from the EXPLORATIONS Book:
Advanced Placement Statistics with the TI-89

Lessons

# Summarizing Distributions of Univariate Data

Activity Overview

Students understand statistical concepts like center of data and the amount of data variation from the center. They calculate the measures of the center of a distribution and the measures of spread for the data collected as a list. Students also create boxplots for the data. They examine the effects of changing units on summary measures.

Before the Activity

Install the Statistics with List Editor application on the calculator using one of these two methods:

• TI Connect™, a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™  "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 37 - 48 from the attached PDF file for your class
• During the Activity

Distribute the pages to the class.

• Enter the data of building heights as lists
• Find the mean, median, range, interquartile range, and standard deviation
• Drop the largest value from the list and calculate the mean, median, range, interquartile range, and standard deviation for the new data
• Notice that the median and the interquartile ranges are more robust than the mean, range, and standard deviation
• Calculate the standard scores (z scores) and determine the number of standard deviations a value is from the mean
• Sort the data in ascending order and calculate the 25th, 50th, 75th, and 90th percentile values
• Find the percentile value of a given number
• Examine the boxplot for the data
• Determine the percent of data in different regions of the plot
• Change the units for the data and observe the effects on summary measures
• After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary