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Analyzing Data Word Problems

This lesson shows how to solve word problems that ask questions about data shown in tables, bar graphs, and pictographs, using comparative language and simple addition or subtraction to find the answer.

What Are Data Word Problems?

A data word problem gives you information in a table, a bar graph, or a pictograph, and then asks a question in words that you must answer using that information. Instead of just reading a chart, you have to think about what the question is really asking, pull out the right numbers, and then use math like addition or subtraction to find the answer.

Before you can analyze data in a word problem, the data usually has to be organized first. If you want a refresher on how information is gathered and sorted into categories, take a look at collecting data. This lesson focuses on the next step: using an organized data display to answer real questions.

Reading the Data Display

Data word problems can show information in more than one way. The three most common displays are:

Tables, where numbers are listed in rows and columns.
Bar graphs, where the height or length of a bar shows a count.
Pictographs, where small pictures represent a value, and sometimes one picture stands for more than one item.

No matter which display a word problem uses, your first job is the same: figure out exactly what number each part of the chart represents before you try to compare or combine them.

Example Data: Favorite Fruit Survey

Suppose a class was asked to name their favorite fruit, and the results were recorded in this bar graph.

Figure 1: Number of students who chose each fruit as their favorite.

Using Comparative Language

Many data word problems use words that compare amounts, such as "more than," "fewer than," "the most," "the least," or "the same as." These words tell you which operation to use. If a problem asks how many more students chose apples than grapes, you subtract: \( 8 - 3 = 5 \), so 5 more students chose apples. If a problem asks for a total, like how many students chose apples or bananas altogether, you add: \( 8 + 5 = 13 \). A closer look at how these comparing words work is available in comparative language.

A Step-by-Step Strategy

Use these steps whenever you see a data word problem:

Read the question carefully and underline or note exactly what it is asking for.
Find the numbers you need in the table, bar graph, or pictograph. Watch out for pictographs, where each picture might represent more than one item.
Decide whether the question needs addition (combining groups or finding a total), subtraction (finding a difference), or simply picking out the largest or smallest value.
Do the calculation and label your answer, since a number alone does not answer a word problem.
Check your answer against the original data display to make sure it makes sense.

Worked Examples

Example 1: How many more students chose apples than grapes?

From the bar graph, apples were chosen by 8 students and grapes by 3 students. Since the question uses "more than," subtract: \( 8 - 3 = 5 \). Five more students chose apples than grapes.

Example 2: How many students chose either bananas or grapes?

Bananas were chosen by 5 students and grapes by 3 students. Since the question asks for a combined total, add: \( 5 + 3 = 8 \). Eight students chose bananas or grapes.

Example 3: Which fruit was the least popular, and how many fewer students chose it than the most popular fruit?

Comparing all three bars, grapes had the fewest votes at 3, and apples had the most at 8. The difference is \( 8 - 3 = 5 \), so grapes were chosen by 5 fewer students than apples.

Common Mistakes to Avoid

A frequent error is misreading a pictograph key, for example forgetting that one picture might stand for two or five items instead of one. Another common mistake is choosing the wrong operation, such as adding when a problem asks how many more, or subtracting when it asks for a combined total. Always reread the question after finishing the calculation to make sure the operation you chose actually matches what was asked.

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