Collecting Data with Tally Charts and Surveys

Before we can make a graph or answer a question about a group of people or things, we need information. Gathering that information is called collecting data. Data can come from asking a survey question ("What is your favorite fruit?"), counting objects, or observing something happening around us.

Once data is collected, it needs to be organized so it is easy to read. The simplest way to organize data by hand is with tally marks arranged in a tally chart.

A tally mark is a single line that stands for one response or one item counted. Instead of writing every mark separately when the count gets large, tally marks are grouped in bundles of five: four vertical lines, then a fifth line drawn diagonally across the first four. Grouping by five makes it much faster to count a large tally chart at a glance, since you can count the bundles by fives and then add any leftover single marks.

Suppose a class of 20 students is asked, "Which fruit do you like best: apples, bananas, or grapes?" As each student answers, one tally mark is added next to that fruit. After everyone has answered, the tally chart below shows the organized results.

Notice how each group of five tally marks is bundled together with a diagonal line. Counting by fives and then adding the extra single marks makes it quick to check that \( 7 + 4 + 9 = 20 \), which matches the number of students surveyed. That check is an important habit: it confirms no response was missed or counted twice while collecting data.

Whenever you collect data, it helps to follow the same steps every time:

1. Decide on a clear question to ask or something specific to observe.
2. List the possible categories of answers ahead of time, such as the fruit choices above.
3. Record each response with a tally mark as it comes in, grouping every fifth mark.
4. Add up the tally marks in each category to find the total for that group.
5. Check that all the totals add up to the total number of people or items counted.

A tally chart is useful on its own for comparing groups quickly, for example seeing that grapes were the most popular fruit and bananas were the least popular. Comparing totals like this often uses comparative language such as "more than," "fewer than," or "the same as."

Once data is organized in a tally chart, it can be turned into a picture that is even easier to read. The same fruit survey could be shown as a bar graph, where the height of each bar matches the total in the tally chart, or as a pictograph, where a small picture stands for a set number of responses. Collecting and organizing data carefully is also the first step toward answering questions about chance, which comes up again in probability word problems.

When practicing with a tally chart worksheet or a tally mark worksheet, always start by counting the total number of tally marks in a row before writing the total, rather than guessing from the pattern. Double-check groups of five carefully: a common mistake is miscounting a bundle as six marks instead of five. Reading the finished chart out loud, saying each category and its total, is a good way to confirm the data was collected and organized correctly before moving on to a graph.

Related lessons

• Math 2