Activity: First Digit Phenomenon

A Descriptive Statistical Discovery

Instruction Sheet

Introduction: Statisticians divide their subject into two major branches.

Descriptive Statistics: Based on the concepts and methods necessary to organize and summarize data, which deals with describing data in the form of tables, graphs, or sample statistics

Inferential Statistics: Is how to reach decisions about a large body of data by examining only a small part of the data, by dealing with inferring (or estimating) population characteristics from sample data

At times we tend to downplay the category of descriptive statistics perhaps thinking it plays a minor role in making decisions and judgment calls or that it lacks the "clout" of inferential statistics. Specifically this spreadsheet activity provides students an opportunity to use simple side-by-side bar graphs to aid in their discovery of the amazing First Digit Phenomenon, while generally it helps them gain an appreciation for shapes of sampling distributions.

This Activity in based on material covered in Units 5C and 6A

Estimated Time for Completion:

This activity could potentially be broken in two parts:

1) a gathering of population data accompanied by the analysis.
2) an internet search accomplished by a modification of the lift-hand theoretical distribution with the ensuring discussion questions.

The total amount of time spent on the activity is fairly variable, approximately 1 to 3 hours for the spreadsheet and analysis, depending on the student in depth taken and background with Spreadsheet. Student can save a considerable amount of time by having the right-hand table and graph previously set up in the Template.

Objectives:

The Mathematical objectives of the activity are:

1. To discover through U.S. Census data, the distributions of both the right-hand and left-hand digits and how they dramatically differ.

2. To learn about the First Digit Phenomenon, its history, and some of the possible applications of Benford's Law.

The spreadsheet objectives of the activity are:

1. To learn using Excel ‘left', ‘right', and ‘countif' functions and how to sort data.
2. To construct bar graphs and draw appropriate conclusions from the data.

Materials Required:.

- Access to the internet to gather population data from the U.S. Census Bureau's website and do a brief keyword search on "Benford's Law" and /or "first digit phenomenon".

- Access to spreadsheet software

- The project template "First_Digit_Phenomenon.xls".

- A selected states to analyze the distribution of the left and right-hand digits of the City and Town Populations states chart is provided.

- This activity handout for recording, analyzing, and discussing the results.