Dot Plots and Frequency Tables

When we collect data, it is often just a messy list of numbers. To make sense of it, we use tools like frequency tables and dot plots to organize and visualize the information so we can easily spot patterns.

Frequency Tables

A frequency table shows how many times each value occurs in a data set. The "frequency" is simply the count.

For example, consider this set of test scores: $3, 4, 4, 5, 5, 5, 6, 6, 7$.

We can organize this into a frequency table by listing each unique number and counting how many times it appears:

• Value $3$: Frequency $1$
• Value $4$: Frequency $2$
• Value $5$: Frequency $3$
• Value $6$: Frequency $2$
• Value $7$: Frequency $1$

To find the total number of data points, just add the frequencies together: $1 + 2 + 3 + 2 + 1 = 9$.

Dot Plots

A dot plot takes the data from a frequency table and displays it visually on a number line. For every time a number appears in the data set, you draw a dot above that number on the line.

Using the same example, you would draw a number line from $3$ to $7$. You would place one dot above the $3$, two dots stacked vertically above the $4$, three dots stacked above the $5$, and so on. This creates a visual "mountain" of data that makes it easy to see where most of the values are grouped.

Describing the Shape of the Data

Once you have created a dot plot, you can describe the shape of the data distribution by looking at how the dots are arranged.

• Symmetric: The left and right sides of the dot plot look like mirror images. Our example above is symmetric, peaking right in the middle at $5$.
• Skewed Left: The "tail" of the data stretches to the left. This means most of the dots are clustered on the right side of the number line, with a few low values trailing off to the left.
• Skewed Right: The "tail" stretches to the right. Most of the dots are clustered on the left side, with a few high values trailing off to the right.

Special Features

You should also look for specific features within the data set:

• Clusters: Groups of data points that are packed closely together.
• Gaps: Empty spaces on the number line where there are no data points.
• Outliers: Data values that are unusually high or unusually low compared to the rest of the group. For example, if our data set was $3, 4, 4, 5, 5, 5, 6, 6, 7,$ and $20$, the number $20$ would be an outlier because it sits far away from the main cluster of data.