Creating Graphs: How to Make a Bar Graph and More

Creating a graph means turning a set of numbers into a picture that shows a pattern, comparison, or trend at a glance. Before you can draw anything, the data usually needs to be collected and arranged in a table or list, which is exactly the skill covered in organizing data. Once the data is organized, creating the graph is just a matter of choosing the right graph type, setting up a scale, and plotting the values accurately.

This lesson focuses on the building side of graphing: how to make a bar graph, how to build a line graph on the coordinate plane, and how to pick the graph type that fits your data. Once a graph is built, the next skill is reading it back out, which is covered separately in interpreting graphs.

Different kinds of data call for different graphs. Here are the four you will use most often.

• Bar graph: compares amounts across separate categories, such as favorite fruits or votes for class president. Categories go on one axis and amounts on the other.
• Line graph: shows how a quantity changes over a continuous variable, usually time. Points are connected by line segments to show a trend.
• Circle graph (pie chart): shows how a whole is split into parts, using percentages or fractions of a full circle.
• Pictograph: uses repeated pictures or symbols, where each symbol stands for a set number of items.

Bar graphs and line graphs are the two you will build most often in Math 1, so the next two sections walk through each one step by step.

Suppose a class survey asked students to name their favorite fruit, and the tally came out to: apples, 4 votes; bananas, 7 votes; cherries, 3 votes; grapes, 6 votes. Here is how to turn that table into a bar graph.

1. Draw a horizontal axis and a vertical axis, meeting at a corner.
2. Label the horizontal axis with the categories (apples, bananas, cherries, grapes).
3. Choose a scale for the vertical axis that comfortably fits the largest value. Here the largest value is 7, so counting by 2s up to 8 works well.
4. Draw one bar per category, with its height matching the value on the scale.
5. Leave equal gaps between bars, and give the graph a title.

Notice that the height of each bar lines up exactly with its value on the scale. If a value falls between two gridlines, such as an odd number on a scale that counts by 2s, the bar's top edge sits halfway between those lines.

A line graph starts the same way a point on the coordinate plane does: with an ordered pair \( (x, y) \). To build a line graph, plot each data point, then connect the points in order from left to right.

As an example of plotting points that follow a rule, consider the equation \( y = 2x + 1 \). Choosing a few values of \( x \) and computing \( y \) gives points such as \( (-1, -1) \), \( (0, 1) \), and \( (2, 5) \). Plotting these points and drawing a straight line through them creates the graph below.

The same process works for real data, such as a plant's height measured each week. Instead of computing \( y \) from an equation, you read each pair of values straight from the data table, plot the points, and connect them to show the trend over time.

Before drawing anything, ask what kind of data you have.

• If the data falls into separate categories (colors, names, types of pets), a bar graph is usually the best choice.
• If the data changes continuously over time or another ordered variable, a line graph shows the trend more clearly.
• If the data represents parts of one whole (percentages that add up to 100), a circle graph fits best.

Picking the wrong graph type will not always give a wrong answer, but it usually makes the data harder to read, which is the opposite of what a graph is for.

A few habits make every graph you build more accurate and easier to read.

• Always title the graph and label both axes, including units where they apply.
• Keep the scale on each axis evenly spaced, counting by the same number every time.
• Double check that the tallest bar or highest point still fits inside the graph before you finish drawing.
• Line up bars and points carefully with the gridlines rather than estimating by eye.

Working through graphing worksheets and graphing activities with different data sets is the best way to build speed and accuracy. Once you are comfortable creating graphs, the natural next step is learning to read trends, comparisons, and outliers back out of a finished graph.

Related lessons

• Math 1