Statistics Today

According to the American Statistical Association, statistics is the scientific application of mathematical principles to the collection, analysis, and presentation of numerical data. Statisticians design surveys and experiments; collect, process, and analyze data; and interpret the results. Statisticians also work with experts in other fields. For example, statisticians can provide guidance in determining what information is reliable and which predictions can be trusted. They often help search for clues to the solution of scientific mysteries and can keep investigators from being misled by false impressions. The application of statistics can lead to a better and more complete understanding of the world and human activity.

Based on the statistics taught in their K–12 mathematics classes, students should gradually come to believe and understand why:
• Data beat anecdotes
• Variability in data is natural, predictable, and quantifiable
• Random sampling allows results of surveys and experiments to be extended to the population from which the sample was taken
• Random assignment in comparative experiments allows cause-and-effect conclusions to be drawn
• Association is not causation

Here we provide you with tools to help your 6–8 students develop a conceptual and practical understanding of statistical concepts and processes.

From the ORC Collection

## Lessons and Activities

In Exploring Histograms (ORC #1458, grades 5–9), students calculate mean, median, and mode and can use an applet to explore how the length of the interval affects the shape of a histogram and how outliers do or do not affect the measures of center. For more lesson ideas, see Histograms and Bar Graphs (ORC #5098, grades 6–8).

State Names (ORC #5284, grades 5–8) explores the frequency of letters that occur in the names of the 50 states. Students represent these frequencies using a bar graph, stem-and leaf plot, and box-and-whiskers plot.

We're All Tuned In (ORC #274, grades 5–10) offers students a peek into how advertising agencies gather and use data to identify trends and to make recommendations to a client.

The rich problem presented in Boxes and Cats: Statistics from the Beginning (ORC #9710, grades 5–8) challenges students to consider the question, Why is a box like a cat? Students collect data and learn how to represent the results using box-and-whiskers plots and stem-and-leaf plots. An extension of the problem and a complete discussion of the underlying statistical ideas are included.

The rich problem What Is the Average Birth Month? (ORC #10113, grades 8–10) will engage students in analyzing data and exploring the meaning of "average" month. This problem is designed to lead students to a deeper understanding of basic statistical concepts.

Representation of Data—the U.S. Census (ORC #9741, grades 6–8) provides another rich problem. Students analyze an illustration that presents data from the 1930 and the 1960 censuses to see what inferences they can draw from the data displays.

The news stories in NewsHour Extra: Economics (ORC #2255, grades 7–12) provide background and ideas for classroom lessons applying economics, mathematics, and statistics related to contemporary issues and newsworthy situations.

The unit Collecting, Representing, and Interpreting Data Using Spreadsheets and Graphing Software consists of two lessons: Collecting and Examining Weather Data (ORC #1442) and Representing and Interpreting Data (ORC #1443). In the lessons, students in grades 3–7 compile weather data on a spreadsheet and then use the spreadsheet's graphing function to analyze and interpret the data.

In Representing Data: Whale Weight (ORC #4214, grades 6–8), students examine the relationship between the length and weight of a whale. They perform simple unit conversions and use proportional reasoning to complete a table of the lengths and weights of whales and determine if the results can be generalized.

Accessing and Investigating Population Data features two lessons—National Population Projections (ORC #1135) and State Population Projections (ORC #1136)—in which students in grades 5–7 use the U.S. Census Bureau to investigate and analyze population data and trends. They also create graphs to compare and contrast information.

Exploring Linear Data (ORC #3324, grades 8–12) lets students collect data and model linear data by constructing scatterplots. The students interpret data points and trends and investigate the line of best fit.

Functions Derived from Data (ORC #10127, grades 8–12) presents another rich problem. The activities focus on identifying the type of function a data set might represent, finding the symbolic representation of a function through pattern building, and looking at behaviors of functions through a variety of real-world contexts.

Go to Math: Misleading Graphs (ORC #6522, grades 5–8) to find examples of misleading graphs that illustrate how information can be distorted and misrepresented.

## Resources for Students

Set your students loose on the U.S. Census Bureau website or the Quick Facts page. See what they can find out about your area or any other area of the country!

Mean and Median is an interactive histogram applet. When the students input the data forming the histogram, all the displayed statistical measures including standard deviation are updated.

Handling Data is an introductory statistics tutorial appropriate for middle school students or anyone beginning to study statistics. Find more interactive mathematics activities from the BBC at KS2 Bitesize for students ages 7–11 and at KS3 Bitesize for students ages 11–14.

Salaries: Math Challenge #29 addresses the question, Will women ever earn as much money as men? It is one of eighty challenging mathematics activities developed for middle school students by the National Council of Teachers of Mathematics.

Have your students go to the American Statistical Association Career Center to learn more about what statisticians do, how to become a statistician, and in what industries statisticians are employed.

Histogram is an easy-to-use, interactive tool for creating histograms and box plots. To find other useful, grade-appropriate tools for engaging students in learning, go to the National Library of Virtual Manipulatives.

## Background Resources for Teachers

Data Analysis, Statistics, and Probability is an online college-level course for elementary and middle school teachers. It features practical examples designed to develop the learner's understanding and use of data. A glossary of statistical terms is included.

What Is a Survey? is an online ten-chapter booklet written for the layperson. It provides everything you need to know about surveys, from survey methods to the meaning of margin of error.

The NCTM article Engaging with the Art & Science of Statistics explores the art and science of statistical thinking.

This introduction to the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Report: A Pre-K–12 Curriculum Framework makes the case for incorporating statistics into the pre-K–12 curriculum to ensure the development of statistical literacy for today's high school graduates.