Math Background

Working With Data: Overview

Imagine reading through thousands of pages of data collected from the last census: number of people in the household, age, nationality, household income, address, and so on. How can all that data make sense? This question leads to fun classroom activities that deal with gathering data, displaying data, and summarizing and organizing data. It also links mathematics to the real world. Welcome to the world of mathematics known as statistics.

How is data collected? Questionnaires, interviews, and telephone surveys are just a few of the ways that data is gathered. From these collections, tallies, graphs, and line plots are created to help reduce the data into meaningful visual presentations.

However, if data is merely collected and displayed, we are missing the most important feature: analysis of the collected data. Analysis allows us to summarize and organize, and even make predictions. Analyzing data is essential for the growth of students' mathematical understanding.

Lead students to realize the need for identifying numbers that can accurately represent the entire data set. These numbers, called measures of central tendency, help to condense data into a few numbers. This process of analysis begins in Grade 2 by analyzing the spread in the numbers, from lowest to highest. This is known as the range. Another descriptive concept covered at this level is the piece of data that occurs most frequently. This is known as the mode.

Let's look at an example. The table shows the number of tickets sold at a theater in one week.

table

Notice that the number of tickets sold varied from 23 on Wednesday to 96 on Saturday. This means that the range of the data is 96 − 23, or 73 tickets. Also notice that on Friday and Sunday the same number of tickets were sold. This means that 65 is the mode; it occurs most frequently. (If a different number of tickets were sold each day, we would say that there was no mode.)

As concepts are developed, help students to connect concepts they learned last year to concepts they are learning this year. Last year, they represented and compared data using tally marks, tables, pictographs, and bar graphs, in addition to learning about range and mode. They also answered questions about a survey. This year they will collect and record data using line plots, pictographs, bar graphs, and tables.


Houghton Mifflin Math Grade 3