Comparative Language for Comparing Data in Bar Graphs

Comparative language is the set of words and phrases we use to compare two or more amounts. In everyday speech you might say a backpack is "heavier than" a lunchbox, or that Tuesday had "more" rain than Monday. In math, these same words let us describe and compare data shown in tables, bar graphs, and pictographs. Learning to recognize comparative language is an important step after collecting data, because once information is gathered, we need the right vocabulary to talk about what it shows.

Here are some of the most common comparative words you will see in math problems, along with what they mean when comparing two quantities.

A comparative bar chart makes it easy to see differences at a glance, because taller bars stand for bigger amounts. When you read a bar graph comparison, look at the height (or length) of each bar and match it to comparative words. For example, in the graph below, a survey asked students to pick their favorite fruit.

Using comparative language, we can say grapes received "more votes than" apples, and bananas received "the fewest votes." Grapes have the "most" votes overall. If a question asks how many more votes grapes received than bananas, we subtract: \( 8 - 4 = 4 \). Grapes received 4 more votes than bananas. This kind of bar graph comparing two things (or more) is exactly what a comparative bar chart is built to show. For more practice building and reading these charts, see the lesson on bar graphs.

Comparative language works the same way with pictographs, except instead of comparing bar height, you compare the number of symbols. If each picture stands for one item, count the symbols in each row and use words like "more than," "fewer than," or "equal to" to describe what you find. If each symbol stands for more than one item, you may need to multiply before comparing. To review how symbols represent quantities, check out the lesson on pictographs.

Sometimes a data set has three or more categories, and a question asks you to find the group with the most or the least. To answer, list every amount, then order them from smallest to largest. The largest value earns the word "most" or "greatest," and the smallest value earns "least" or "fewest." Using the fruit survey above, the order from least to most votes is bananas (4), apples (6), and grapes (8).

A class recorded the number of pets owned by three groups of students: Group A has 5 pets, Group B has 9 pets, and Group C has 5 pets. Answer the following using comparative language.

Which group has the most pets? Group B, with 9 pets, has more pets than Group A or Group C.

Which groups are equal? Group A and Group C both have 5 pets, so they are equal to each other.

How many more pets does Group B have than Group A? \( 9 - 5 = 4 \). Group B has 4 more pets than Group A.

Comparative language shows up constantly in word problems, especially once data is displayed in graphs. Being comfortable with phrases like "more than," "less than," and "the same as" also helps when working through probability word problems, where you often compare the likelihood of different outcomes using this same vocabulary. The more familiar you become with these comparison words, the easier it becomes to interpret any graph or data set you encounter.

Related lessons

• Math 2