The following two-part multiple-choice question, explained here in hopes of helping algebra 1 students and their parents in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s Spring 2016 test for algebra 1 (#25):
A real estate agent recorded the home prices, in thousands of dollars, for 50 randomly selected homes in two communities, A and B. The dot plots display the recorded data.
Which statement best describes the relationship between the home prices in community A and community B?
A. The homes in community A are typically more expensive and more consistent in price than those in community B.
B. The homes in community A are typically more expensive and less consistent in price than those in community B.
C. The homes in community A are typically less expensive and more consistent in price than those in community B.
D. The homes in community A are typically less expensive and less consistent in price than those in community B.
Which of the listed home prices most likely represents the third quartile for the 50 home prices in community B?
Analysis of this question and online accessibility
The question is valid in that it tests students’ ability to evaluate the central tendency and spread of data plotted on a dot plot.
The question can be delivered online or on paper. However, as shown, the question is better tested on paper than online, since reading the same long sentence for each option choice in part A, with just two little words changed, may lead to errors in responding. With an online test delivery platform, which is how most students take the PARCC test, the question in part A is better delivered using drop-down menus for the words less and more. As a result, validity and reliability measures for the item may differ under different test-taking environments.
No special accommodation challenges can be identified with this question, so the question is considered fair.
Resources for further study
Purple Math, developed by Elizabeth Stapel, a math teacher from the St Louis area, has developed a nice page dealing with the interquartile range. Her explanation is a little different from mine, because she uses box-and-whiskers plots. Her lesson begins here.
In addition, Sal Khan, an engineer who developed the Khan Academy, a set of thousands of tutorial videos about math and a few other subjects, has created a nice written essay about choosing the most appropriate measure of central tendency, between mean and median, given characteristics of the data, beginning here.
Ron Larson, Laurie Boswell, Timothy D Kanold, Lee Stiff. Algebra 2, Illinois edition. Evanston, Ill.: McDougal Littell, a division of Houghton Mifflin Company, 2008. The book is used in several algebra classes taught in Illinois high schools.
Foerster, Paul A. Algebra and Trigonometry: Functions and Applications, revised edition. Addison-Wesley, 1980, 1984. The book is used in several algebra classes taught in middle and high schools in both Illinois and Maryland.
Purpose of this series
To help algebra 1 students and their parents prepare for the PARCC test in math, as administered in at least six states, or to just master content on that test, we provide an analysis of every algebra 1 math problem PARCC released in 2016. The series can be found here.