Math Background

Graphing Data: Overview

Your children are already familiar with gathering data—for example, in class surveys, they have been asked to raise their hand if a dog is their favorite animal or if baseball is their favorite sport. In Grade 1, they learned how to gather and organize data from such surveys into tally charts. Then, using the tally charts, they learned to display the data in picture graphs and bar graphs with a scale of one. Once children have reviewed these skills, they will be ready to learn to analyze and compare data at a more advanced level. In this chapter they will compare data in tables and charts, read pictographs and bar graphs with a scale of one or greater, and create bar graphs. They will also be introduced to the statistical measures of range and mode.

You may begin by reintroducing tally charts as a means of collecting and organizing data. The data in a tally chart are clearly understood, displayed in easy-to-count groups of five. A simple classroom survey about children's favorite pets can be used to reinforce the connection between a tally chart and the information collected. When children see that one tally mark is made for each child's vote, they will understand how to use tally marks to collect and organize data.

Tally chart

Once children have reviewed how to make and read tally charts, they learn to interpret and compare different-sized data sets displayed in a tally chart or a table.

Next, children will be reintroduced to pictographs. Pictographs use pictures to represent data, making it easy to compare data visually. To read a pictograph, children start by looking at the key to see how many of a given item each picture stands for. At this level, they will be working with graphs with a scale of one, two, or five, meaning each picture represents one, two, or five of that item. Once children know what each picture stands for, they can count the number of pictures in each category by ones, twos, or fives to tell how many there are of each item. Once children understand what each picture stands for, they will be able to compare and analyze the data to determine which categories have more or less, to find out how many more or less there are of one group, or to find the total number of items in more than one group.


In Grade 1, children were taught to read and make simple pictographs with a scale of one. At that level, pictographs were referred to as picture graphs.

Once children have experience working with pictographs, they will move on to bar graphs. While pictographs are a “semi-concrete” way of representing data, bar graphs are more abstract. Instead of representing data by using pictures, bar graphs use colored bars on a grid with corresponding numbers to represent how many are in each group. Children will learn that they can find how many by looking at the number where each bar ends. Bar graphs allow children to more easily find the number of items in each group by using the numbers instead of counting.

Favorite Pets Chart

Children will learn to make and analyze their own bar graphs based on data given to them in a tally chart or a table. Working from a tally chart or a table helps children to see that data can be displayed in different ways. It also helps them make the connection between the tallies in a chart or the numbers in a table and the number of colored boxes on the graph. Although children learned to read bar graphs with a scale of one or two, they will only make graphs with a scale of one in which one box represents one item or vote. As they did with pictographs, children will learn how to use bar graphs to compare information, such as which group has the most or least, how many more or less there are of one group than another, or how many there are in two or more groups.

Finally, children will be introduced to the statistical measures of range and mode through tally charts and corresponding line plots. Line plots organize numerical data along a number line. Examples of numerical data that children might deal with at this level are the shoe sizes of a group of children, the number of siblings or pets of a group of children, and the points scored in a game by a group of children. The numerical categories in the left column of the tally chart are the same as the numbers displayed along the number line of the line plot. For each tally in the chart, one X is placed above the corresponding number on the line plot. So for a survey of the number of siblings that a group of children have, the tally chart might have the categories zero through four, representing children with zero to four brothers and sisters. You may wish to adjust the numbers for those with more than 4 siblings or label the last category 4 or more. The number line on the line plot would also run from zero to four. The number of students who have no brothers or sisters would be recorded as tallies in that row of the chart and as X's above the zero on the line plot.


Although children have not seen a line plot before, their knowledge of tally charts will help them understand how line plots are organized. Conducting a simple class survey can help children to understand the relationship between the number of tallies in the tally chart and the number of X's on a line plot. Once they understand this, they can find the range of the data by subtracting the least number from the greatest. In the line plot shown above, you would find the range by subtracting zero from four. Mode is often easier for children to find and understand. The mode of a data set is the category that has the most votes or the number that appears most often. In the line plot shown above, the most children have 2 siblings, so 2 is the mode.

Once children have gained proficiency in using tally charts, pictographs, and bar graphs, they will focus on using graphs as a means to solve problems. Analyzing graphs to get information for problem solving demonstrates children's understanding of how a graph is organized and what it represents. Children can also write questions based on the information given in a graph. By writing questions, children reinforce their understanding of what a graph shows.

Houghton Mifflin Math Grade 2