Frequency Tables and Dot Plots

When you collect raw data, whether it's the number of siblings each student has, the colors of cars in a parking lot, or the scores on a quiz, the numbers usually arrive in a messy, unordered list. A frequency table is a simple tool that organizes that raw data by listing every distinct value along with how many times, or how frequently, it occurs.

Most frequency tables have three columns: the data value, a set of tally marks used to count occurrences, and the total frequency (the count itself). Once your data is organized this way, patterns that were hidden in the raw list suddenly become easy to see.

Suppose you survey 12 students and ask how many siblings they have. Here is the raw data, in the order it was collected:

0, 1, 1, 2, 1, 3, 2, 0, 1, 4, 2, 3

To build a frequency table, go through the list one number at a time and add a tally mark next to that value. Tally marks are grouped in sets of five (four vertical lines with a fifth line crossing through) so the final count is fast to read.

Adding the frequency column gives \(2 + 4 + 3 + 2 + 1 = 12\), which matches the original 12 students surveyed. Checking that the frequencies add up to the total number of data points is always a good way to catch tally mistakes.

A dot plot is a graph that shows the same information as a frequency table, but visually. Each data value gets its own position on a number line, and one dot is stacked above that position for every time the value appears. The taller the stack of dots, the more frequently that value occurred.

Dot plots work best for small, discrete data sets like the sibling survey above, since every single data point is shown as an individual dot rather than being grouped into ranges.

Notice that the dot plot above is built directly from the frequency table: the value 0 has a frequency of 2, so two dots are stacked above 0; the value 1 has a frequency of 4, so four dots are stacked above 1, and so on. Once the frequency table is complete, drawing the dot plot is just a matter of stacking the correct number of dots above each labeled value on the number line.

This makes the two tools a natural pair: the table gives you exact counts, while the dot plot lets you instantly see the overall shape of the data, where it clusters, and whether any values stand apart from the rest. For a deeper look at describing that overall shape (symmetric, skewed, or with outliers), see shapes of distributions.

Frequency tables and dot plots are usually the first step toward more advanced displays. Once a data set has many possible values, it often makes more sense to group values into intervals and build a bar-style graph instead, which is exactly what frequency distribution and histograms covers. If you're deciding which type of chart best fits your data at all, it also helps to review the advantages and disadvantages of different graphs.

A teacher records the number of pets owned by each student in a class of 10 students:

1, 0, 2, 1, 1, 3, 0, 2, 1, 0

Step 1: List the distinct values: 0, 1, 2, 3.

Step 2: Tally each occurrence.

Step 3: Check the total: \(3 + 4 + 2 + 1 = 10\), which matches the 10 students. The data checks out.

Step 4: To turn this into a dot plot, draw a number line from 0 to 3, then stack 3 dots above 0, 4 dots above 1, 2 dots above 2, and 1 dot above 3, exactly as shown in the earlier example.

Related lessons

• Statistics Help