# Measures of Location

• ### Poem: Expected Value Haikus

This haiku collection by Lawrence Mark Lesser from The University of Texas at El Paso was written in 2020 and won second place in the 2021 A-mu-sing Competition.  Each haiku in the collection addresses some property or real-world application of expected value that can be explored in class: the math and psychology in the structuring of an internationally syndicated game show (Deal or No Deal), tree diagrams (that students can do a calculation to verify in a realistic popular context of college basketball, showing how the EV need not correspond to the most likely outcome), an engaging probability paradox (in the context of the most popular animal Americans own as pets), the interaction with utility when making consumer decisions, a concrete visual analogy for a distribution’s expected value (inspired by Figure 2 of Martin’s July 2003 JSE article), and the concept of an estimator’s bias, and the how EV and mean express the same idea but in different contexts (random variable versus a sample, population or probability distribution).

• ### Song: Trimmed Mean

A song about the trimmed mean as a robust measure of distributional center.  The lyric was written by Dennis Pearl from Penn State University in May 2023 and may be sung to the tune of the KitKat jingle - music by Michael A. Levin and lyric by Ken Shuldman used in the KitKat candy bar advertisements since 1986.

• ### Song: X-bar 12-bar Blues

A song video about major conceptual properties of the mean, as identified in the statistics education literature. Music and lyrics (c) 2018 Lawrence M. Lesser, where Verses 2,3,4, and 7 use properties from Strauss & Bichler's 1988 JRME article while Verses 5 and 6 use concepts listed in Pre-K-12 GAISE Report.

• ### Introduction to Statistics (NASA Lesson)

These pages explain the following basic statistics concepts: mean, median, mode, variance, standard deviation and correlation coefficient (with example from the Institute on Climate and Planets).

• ### Using Computers for Statistical Analysis (NASA Activity)

This lesson introduces students to creating spreadsheets for statistical analysis.

• ### Team Extreme: The Statistics of Success (NASA Activity)

This program focuses on the teamwork required to produce a successful mission and the importance of statistics in project design and management. Using the video and a hands-on lesson, students learn about statistical analysis and how people use statistics, such as mean, median, mode and range, to make decisions. Members of the Penske Racing Team and engineers from Pratt & Whitney Rocketdyne help students investigate the relationship between work, energy and power as they look at race car design, the space shuttle and the International Space Station.

• ### A Dusty Dilemma (NASA Activity)

The Student Dust Counter is an instrument aboard the NASA New Horizons mission to Pluto, launched in 2006. As it travels to Pluto and beyond, SDC will provide information on the dust that strikes the spacecraft during its 14-year journey across the solar system. These observations will advance human understanding of the origin and evolution of our own solar system, as well as help scientists study planet formation in dust disks around other stars.

In this lesson, students learn the concepts of averages, standard deviation from the mean, and error analysis. Students explore the concept of standard deviation from the mean before using the Student Dust Counter data to determine the issues associated with taking data, including error and noise. Questions are deliberately open-ended to encourage exploration.

• ### Song: My Family's Mean

A song for use in helping students to reason about mean and median and the effect of an outlier.  Lyrics & Music © 2016 Amy Adler. This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

• ### Introduction to Descriptive Statistics

This website provides a comprehensive overview of descriptive statistics (mean/median/mode, range, standard deviation, and variance) through informative webpages with examples, links to data sets, and problems for the readers to try for themselves.

• ### Song: Which Measure Should I Choose

A song to be used in discussing how the mean and standard deviation work well in describing symmetric distributions while the median and IQR are valuable when you need more resistant measures for skewed distributions. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of “Faithfully,” the 1983 ballad by the band Journey. Also, an accompanying video may be found at