Analyzing Data with Bar Graphs

Once you know how to read and draw a bar graph, the next step is analyzing what the graph is telling you. Analyzing a bar graph means comparing categories, comparing two or more data sets against each other, and using the numbers on the graph to support a conclusion. This lesson focuses on that comparison and conclusion-drawing process.

Analysis starts with simple comparisons. Once you know the value of each bar, you can ask questions like: Which category has the greatest value? Which has the least? How much bigger is one bar than another? These comparisons turn raw numbers into useful information, such as noticing that one product sold twice as much as another, or that one class read far fewer books than the rest.

Sometimes you need to compare two data sets across the same categories, like two classes' reading habits over the same four days. A double bar graph places two bars side by side for each category, usually in different colors, with a legend showing which color belongs to which data set.

Reading this graph, Class A read 10 minutes on Monday and Class B read 15 minutes. On Tuesday the pattern flips: Class A read 15 minutes and Class B read 10 minutes. On Wednesday, Class A read 20 minutes and Class B read 25 minutes. On Thursday, Class A read 25 minutes and Class B read 20 minutes.

Once you can read individual bars, you can calculate new information the graph does not label directly. To find how much more one bar shows than another, subtract the smaller value from the larger one. On Monday, Class B read more than Class A by \( 15 - 10 = 5 \) minutes. On Wednesday, Class B again read more, by \( 25 - 20 = 5 \) minutes.

To find a total, add up every bar's value for that data set. Class A's total minutes for the four days are \( 10 + 15 + 20 + 25 = 70 \). Class B's total is \( 15 + 10 + 25 + 20 = 70 \). Even though the two classes read different amounts on different days, their four-day totals turned out to be equal. Finding a total also lets you calculate an average, such as dividing the total by the number of days to get 17.5 minutes per day for each class.

A good conclusion is a sentence backed up by specific numbers from the graph, not just a guess. Compare bars to describe trends using words like greatest, least, increased, decreased, or equal. For the reading graph above, you could conclude: "Class A's reading time increased steadily from Monday to Thursday, while Class B's reading time went up and down, but both classes read the same total number of minutes over the four days." Notice how this conclusion points to actual bar values instead of a vague impression.

When you compare two data sets, also check whether one is consistently higher, or whether the two sets trade places from category to category, like Class A and Class B do here. Both patterns are useful conclusions, but they describe very different situations.

• Misreading the scale interval, such as assuming each gridline equals 1 unit when it actually equals 10.
• Comparing bars from two different graphs that use different scales, which makes the comparison meaningless.
• Trusting a graph where the value axis does not start at 0, since this makes small differences look much bigger than they really are.
• Writing a conclusion that goes beyond what the data actually shows, such as claiming a cause when the graph only shows a comparison.

Related lessons

• Reading and drawing bar graphs