This handout is intended to help you organize the information about how to read and construct pie, bar, and line graphs. Once you complete this handout, you should be able to name the key features of graphs that help you read them, describe how to use those features to read different types of graphs, and explain how to decide which type of graph is appropriate for a specific set of data.

KEY IDEAS FOR READING GRAPHS

Essential features of pie, bar, and line graphs:

Feature / What it is / Where you find it / How you use it
Source / Information about where the data came from. / Usually above or below the graph. / The source helps you determine how well you can trust the information.
Title / A summary of the information presented in the graph. / Usually above or below the graph. / The title helps you understand the “big picture,” often by describing the 4 W’s: who/what, when, and where.
Units
(or labels) / Descriptions (in words) of the types of information shown / On pie graphs, this is usually in the title. On bar and line graphs, these are usually the labels along the axes. / The units tell you what types of things were measured for the graph, as well as how they’re recorded. Examples are “years,” “countries,” and “profit.” You’ll also see instructions on how to read the information, like “in thousands of dollars” or “years since 2000.”
Categories
(or Scale) / Labels for each of the pieces of the graph. / On pie graphs, these are usually attached to each section of the pie. On bar and line graphs, these are listed along the axes by each bar or line of the grid. / The categories tell you exactly what was measured. For example, if the units are years, you might see 2000, 2001, 2002, etc. For countries, it might be “Canada,” “Mexico,” and “United States.”
Sometimes the categories are just numbers that show the level of detail in the graph, like $1000, $2000, $3000, etc. This is called a “scale.”
Data / The sections, bars, or points shown in the graph. / Usually in the middle of the graph / The data is what you read to make claims or draw conclusions. It’s the reason the graph was created.

How to read individual values from a graph:

Pie Graphs –

  1. Determine the “whole” for the pie – not the number, but the description of the category or object that includes all the parts. This may be in the graph’s title, or you may have to create a description of your own based on all the categories in the pie.
  2. Compare the area and widths of the sections to determine which categories are bigger or smaller than others.
  3. If percentages are given, describe them in words like, “____ % of ______was from _____” where you write the name of the whole in the second blank, and the category name in the third blank.
  4. If a percentage is not given, you can compute it by dividing the amount in a specific section by the total of the values in all sections.

Bar Graphs – The descriptions below are for a graph with vertical bars. Horizontal bars are similar.

  1. Choose a bar you wish to describe. The lengths (heights) of the bars tell you which categories are bigger or smaller than others.
  2. Find the category name for that bar by looking at the end of the bar that sits on the horizontal axis.
  3. Find the amount for that bar by following the bar up to its top, then over to the same height on the vertical axis. Read or estimate the number at that height.
  4. Write a sentence using the number and category name from the previous steps, as well as the units from the vertical axis. If the numbers on the vertical axis are percentages, the title or units on that axis should mention the whole (what you have a “percentage of”).

Line Graphs –

  1. Choose a point on the graph you wish to describe. The heights of the points tell you which categories are bigger or smaller than others.
  2. Find the category name or value for that point by looking straight down from it to the horizontal axis. If it is a number, you may have to estimate it.
  3. Find the amount for your point by looking straight across from it over to the same height on the vertical axis. Read or estimate the number at that height.
  4. Write a sentence using the numbers and/or category name from the previous steps, as well as the units from the two axes. If the numbers on either axis are percentages, the title or units on that axis should mention the whole (what you have a “percentage of”).

Examples:

Look at the title – this pie shows all of the different types of state and local government expenditures. The top two slices are about the same size – that tells me the percentages or amounts are roughly the same. The slice on the top right says “Higher Education 10.5%.” This means “During 2005-2006, Higher Education took 10.5% of all the state and local government expenditures.” / Look at the tallest bar. Below it is the category “GM”, and if I look to the left at the same height, I see it’s a little more than halfway between 3.5 and 4 on the axis. So this bar means “In 2007, GM had approximately 3.8 million new vehicles sold.”

KEY IDEAS FOR CONSTRUCTING GRAPHS

Checklist of essential features to include in your graphs –

Feature / Where you put it / What it should include
Source / Usually above or below the graph. / The individual or organization that provided the data.
Title / Usually above or below the graph. / The 4 W’s: who/what is the data about, when it was obtained, and where (geographically) it was obtained
Units
(or labels) / On pie graphs, this is usually in the title. On bar and line graphs, these are usually the labels along the axes. / Words that describe the types of things that were measured, and how they’re recorded. For example, “Years” or “Profit (in millions of dollars).”
Categories
(or Scale) / On pie graphs, these are usually attached to each section of the pie. On bar and line graphs, these are listed along the axes by each bar or line of the grid. / Words or numberstellingexactly what was measured. They should be evenly spaced, and numeric categories should increase by the same amount every time.
Examples are countries like “Canada,” “Mexico,” “United States,” or years like 2000, 2001, 2002, or money, like $1000, $2000, $3000, etc.
Data / Usually in the middle of the graph / This should be drawn carefully.
  • Sections of a pie should occupy the same fraction of the circle as the percentage that section represents.
  • Axes of bar and line graphs should be straight and form a right angle (an “L”).
  • Heights of bars or points should be accurate with the scale – if the number is a little more or less than a scale line, the height of the point or bar should show that.

The purposes of pie, bar, and line graphs:

Pie Graphs – Used to compare the different parts of a whole. Data is usually pairs of categories and measurements, but the measurements do NOT need to be percentages. Also, if the categories do not make a logical whole, you CANNOT create a pie graph – use a bar graph instead.

Bar Graphs – Used to compare different groups which do not make a whole. Data is usually pairs of categories and measurements (for example, city names and populations).

Line Graphs – Used to show trends (patterns in how things change). Data is usually pairs of numbers, like years and dollars. If the categories do not have a single logical order (for example, city names do not), you CANNOT create a line graph – use a bar graph instead.

How to constructa graph:

Pie Graphs –The description below is for sketching a pie graph by hand. For better accuracy, use Excel.

  1. Once you know your data CAN be made into a pie graph, if your data is not given as percentages, you’ll need to calculate them. First find the numeric “whole” for the pie by adding the values of all parts. Then calculate the percentage for each part by dividing the amount for that part by the whole.
  2. Compare your percentages to fractions of a circle that are easy to picture: 50% = half, 33.3% = a third, 25% = a quarter, 20% = a fifth, 16.7% = a sixth, 12.5% = an eighth, 10% = a tenth, 5% = a twentieth.
  3. Draw your largest section first, with one side of it being vertical from the center to the top of the circle (the “12 o’clock” position). It should open to the right, following the motion of a clock. If your percentage isn’t one of the “easy” percentages, your section should be bigger or smaller than the nearest “easy” fraction of a circle.
  4. Draw your next largest section starting from the end of the last section. It can help to turn your graph so the last section’s end is vertical (at 12 o’clock). Continue until you finish the circle.
  5. Write a title above the graph, put categories and the data values next to each section, and write your source underneath the graph.

Bar Graphs – The descriptions below are for a graph with vertical bars. Horizontal bars are similar.

  1. Draw axes that are straight and make a right angle (an “L”).
  2. Look at the pairs of data and decide which categories are identifiers (“input” values), and which are measurements (“output” values).
  3. Look at the measurements and find the highest and lowest numbers. Choose “nice” numbers (numbers ending in 0’s) that are close to, but below the lowest number and above the highest number. Choose a number you can keep adding and go from the lower “nice” number to the higher “nice” number in about 10 steps. (For example, to go from 7000 to 25000, I could use 2000.)
  4. Put these numbers along the vertical axis, making sure they’re evenly spaced. If you don’t start from zero, put a zig-zag in the vertical axis between where it crosses the horizontal axis and your lowest “nice” number.
  5. Look at the “identifiers” in your data. If they’re numbers, use the same procedure as steps 3 and 4 to set up your horizontal axis. Otherwise, just evenly space the labels.
  6. For each data pair, find the location of the identifier/input on the horizontal axis. Draw a vertical bar centered over that spot with a height matching the measurement/output value from your data.
  7. Write a title above the graph, add unit descriptions to each axis, and write your source underneath the graph.

Line Graphs –

  1. Do steps 1 – 5 from the “bar graphs” instructions.
  2. For each data pair, find the location of the identifier/input on the horizontal axis, go up to the height of the measurement/output, and draw a dot.
  3. Starting from your leftmost dot, draw a curve that connects the dots in order from left to right.
  4. Write a title above the graph, add unit descriptions to each axis, and write your source underneath the graph.

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