Collect and Organize Data Sets

A data set is a collection of values you have gathered from a survey, an experiment, or careful observation. Raw data is messy — a long list of answers in the order they came in. Before you can answer questions like "which option was most popular?" or "how many people responded?" you need to organize the data. Two of the most useful tools for this are the tally chart and the frequency table. Each one converts a raw list into a tidy summary that anyone can read at a glance.

Step 1 — Decide What You Are Counting

• Pick a clear question with a short list of possible answers. "Favorite ice-cream flavor" is a good question; "What is your favorite food?" is too open-ended.
• List every category you expect to see (Strawberry, Vanilla, Chocolate, Mint, Other). Add an "Other" row to catch unusual answers.
• A category that nobody picks still belongs in your chart with a count of 0 — it shows you considered it.

Step 2 — Record Data with Tally Marks

1. Set up a chart with three columns: Category, Tally, Count.
2. Read each response in turn. Add ONE vertical mark in the matching row: |, ||, |||, ||||.
3. For the fifth response in a row, draw a diagonal line across the four vertical marks. That bundle of five is the easiest unit to count later.
4. Continue with new groups of five for the next responses: |||| || means 5 + 2 = 7.
5. When you have read every response, count the marks in each row to get the count.

Step 3 — Build a Frequency Table

• A frequency table has two columns: Category and Frequency. The frequency is just the count from the tally chart written as a number.
• Always include a Total row. The total is the sum of all frequencies and should equal the size of your data set.
• Example: tallies of 4, 3, and 5 give frequencies 4, 3, 5 and a total of 12 — so 12 people answered the survey.
• Frequency tables make it easy to compare categories: the largest frequency is the most popular answer; the smallest is the least popular.

Step 4 — Check Your Work

• Count the raw data list to find the data set size BEFORE you add up the frequencies.
• If the frequencies do not add to the same total, you missed a response or counted one twice — go back through the list.
• Two common mistakes: skipping the diagonal on the 5th mark (so a group of 5 looks like a group of 4) and forgetting to add the "Other" row to the total.