This article explores how statistics can be interpreted in different ways to yield different conclusions. It describes the outcome and discussion of two class activities. In the first, the results are interpreted to "show" that taking a group rather than an individual perspective is ultimately beneficial to the individual. In the second, a variation is added "showing" that telling the truth is better that lying. This resource is from PUMAS - Practical Uses of Math and Science - a collection of brief examples created by scientists and engineers showing how math and science topics taught in K-12 classes have real world applications.

This lesson unit is intended to help you assess how well students are able to: Calculate the mean, median, mode, and range from a frequency chart; and to use a frequency chart to describe a possible data set, given information on the mean, median, mode, and range.

Objectives:

1. Students will know the definitions for mean, median, mode, and range.

2. Given a data set, students will be able to find the mean, median, mode, and range.

This interactive escape room will allow students to practice their skills in mean, median, mode and range. There is also a video over how to solve all of those as well as some notes. 

An example that demonstrates how to calculate the mean of a frequency distribution step by step.  

Students experience data collection, analysis and inquiry in this LEGO® MINDSTORMS® NXT -based activity. They measure the position of an oscillating platform using a ultrasonic sensor and perform statistical analysis to determine the mean, mode, median, percent difference and percent error for the collected data.

Students learn about the statistical analysis of measurements and error propagation, reviewing concepts of precision, accuracy and error types. This is done through calculations related to the concept of density. Students work in teams to each measure the dimensions and mass of five identical cubes, compile the measurements into small data sets, calculate statistics including the mean and standard deviation of these measurements, and use the mean values of the measurements to calculate density of the cubes. Then they use this calculated density to determine the mass of a new object made of the same material. This is done by measuring the appropriate dimensions of the new object, calculating its volume, and then calculating its mass using the density value. Next, the mass of the new object is measured by each student group and the standard deviation of the measurements is calculated. Finally, students determine the accuracy of the calculated mass by comparing it to the measured mass, determining whether the difference in the measurements is more or less than the standard deviation.

This lesson will be a fun way for students to be create and use the collected data to find the measures of central tendency.

Students apply pre-requisite statistics knowledge and concepts learned in an associated lesson to a real-world state-of-the-art research problem that asks them to quantitatively analyze the effectiveness of different cracked steel repair methods. As if they are civil engineers, students statistically analyze and compare 12 sets of experimental data from seven research centers around the world using measurements of central tendency, five-number summaries, box-and-whisker plots and bar graphs. The data consists of the results from carbon-fiber-reinforced polymer patched and unpatched cracked steel specimens tested under the same stress conditions. Based on their findings, students determine the most effective cracked steel repair method, create a report, and present their results, conclusions and recommended methods to the class as if they were presenting to the mayor and city council. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note for details.

Working as if they are engineers aiming to analyze and then improve data collection devices for precision agriculture, students determine how accurate temperature sensors are by comparing them to each other. Teams record soil temperature data during a class period while making changes to the samples to mimic real-world crop conditions—such as the addition of water and heat and the removal of the heat. Groups analyze their collected data by finding the mean, median, mode, and standard deviation. Then, the class combines all the team data points in order to compare data collected from numerous devices and analyze the accuracy of their recording devices by finding the standard deviation of temperature readings at each minute. By averaging the standard deviations of each minute’s temperature reading, students determine the accuracy of their temperature sensors. Students present their findings and conclusions, including making recommendations for temperature sensor improvements.

This 7-minute video lesson gives formulas for the Bernoulli Distribution Mean and Variance. [Statistics playlist: Lesson 42 of 85]

This 4-minute video lesson explains the mean, median, and mode. [Statistics playlist: Lesson 1 of 85]

This 8-minute video lesson gives an example of the mean and variance of Bernoulli Distribution. [Statistics playlist: Lesson 41 of 85]

This 11-minute video lesson looks at the the central limit theorem and the sampling distribution of the sample mean. [Statistics playlist: Lesson 36 of 85]

This 13-minute video lesson provides more discussion of the Central Limit Theorem and the Sampling Distribution of the Sample Mean. [Statistics playlist: Lesson 37 of 85]

Students collect a large set of data (approximately 60 sets) of individual student’s water use and learn how to use spreadsheets to graph the data and find mean, median, mode, and range. They compared their findings to the national average of water use per person per day and use it to evaluate how much water a municipality would need in the event of a recovery from a water shutdown. This analysis activity introduces students to the concept of central tendencies and how to use spreadsheets to find them.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

En este módulo, los estudiantes reconectan y profundizan su comprensión de las estadísticas y los conceptos de probabilidad introducidos por primera vez en los grados 6, 7 y 8. Los estudiantes desarrollan un conjunto de herramientas para comprender e interpretar la variabilidad en los datos, y comienzan a tomar decisiones más informadas de los datos . Trabajan con distribuciones de datos de varias formas, centros y diferenciales. Los estudiantes se basan en su experiencia con datos cuantitativos bivariados del grado 8. Este módulo prepara el escenario para un trabajo más extenso con muestreo e inferencia en calificaciones posteriores.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.