Dot plots and distribution shape
Display each observation and describe clusters, gaps and unusual values.
Before you begin
- Number lines
- Counting frequencies
Give each observation one dot
A dot plot places observations above a numerical scale, stacking repeated values vertically. Choose equally spaced tick marks and label the measured variable and unit. A value repeated three times needs three dots. Count all dots to verify the sample size. Unlike a list of unique values, the plot preserves frequency, showing which measurements occurred most often.
Describe the whole pattern
Look for where observations cluster, whether the two sides are roughly balanced, and whether gaps or isolated points occur. Describe the pattern using the actual variable and units rather than only saying it goes up or down. A gap does not mean missing data unless there is evidence for that interpretation. An unusual observation deserves investigation but should not be deleted simply because it is inconvenient.
Worked example
Make a dot plot for reading times 10, 10, 15, 20, 20, 20 and 35 minutes.
Show the worked solution
- Draw a time axis from 10 to 35 minutes with evenly spaced five-minute intervals.
- Place two dots above 10, one above 15, three above 20 and one above 35.
- Count seven dots. Most times lie between 10 and 20 minutes, with a gap before 35.
7 observations; the largest stack is at 20 minutes, with an isolated 35-minute reading.
Try it yourself
What do four stacked dots above 6 represent?
Common mistakes
- Count repeated measurements separately.
- Use a numerical scale with consistent spacing.
What can you explain now?
For values 2, 2, 3, 5, 5, 5, 8, state the sample size, the most frequent value and the values with no observations between 2 and 8.
Compare with the explanation
7 observations; most frequent value 5; no observations at 4, 6 or 7.
Repeated values still count as separate observations. The empty positions are gaps in this recorded data set.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗