Cluster — Definition, Formula & Examples
A cluster is a group of data values that are bunched closely together, separated from other values in the data set. When you look at a graph, clusters appear as concentrations of dots or bars in one area.
In descriptive statistics, a cluster is a subset of data points that lie near one another, forming a visually distinct concentration within a data display, with noticeable gaps separating it from other groups of data points.
How It Works
To find clusters, look at a graph of your data — such as a dot plot, line plot, or scatter plot — and identify areas where data points are packed closely together. Between clusters, you will see gaps where few or no data points appear. A data set can have one cluster, multiple clusters, or no clear clusters at all. Describing clusters helps you summarize the shape and distribution of data.
Worked Example
Problem: A teacher records the number of books 12 students read over the summer: 1, 2, 2, 3, 3, 3, 8, 9, 9, 10, 10, 10. Identify any clusters in the data.
Step 1: Arrange the data on a number line or dot plot and look for groups of values that are close together.
Step 2: The values 1, 2, 2, 3, 3, 3 form one group between 1 and 3. The values 8, 9, 9, 10, 10, 10 form another group between 8 and 10. There are no values between 4 and 7.
Step 3: The gap from 4 to 7 separates the data into two distinct clusters.
Answer: There are two clusters: one from 1 to 3 books and another from 8 to 10 books, with a gap in between.
Visualization
Why It Matters
Identifying clusters helps you notice subgroups in real data, such as two distinct age groups at a community event or two price ranges at a store. In middle school math and science, describing clusters is a key part of interpreting dot plots, histograms, and scatter plots.
Common Mistakes
Mistake: Confusing a cluster with an outlier
Correction: An outlier is a single value far from the rest of the data. A cluster is a group of several values close together. One isolated point is not a cluster.