Click image to open full size
Dot Plots and Stem-and-Leaf Plots
Simple Displays That Preserve Data
Related Labs
Related Worksheets
Related Cheat Sheets
Dot plots and stem-and-leaf plots are simple ways to organize and display small sets of numerical data. They help students see the shape of a distribution, identify repeated values, and estimate the center and spread of the data. These displays are especially useful when you want to keep the actual data values visible instead of hiding them inside bars or intervals. Learning both methods builds a strong foundation for later topics like histograms, box plots, and measures of center.
A dot plot places a dot above each value on a number line, so stacks of dots show how often values repeat. A stem-and-leaf plot splits each number into a stem, usually the tens place, and a leaf, usually the ones place, so the data stay ordered and easy to read. Because both plots preserve individual values, they are excellent for comparing small data sets and spotting clusters, gaps, and outliers. When the same data are shown in both formats, students can see that each display gives the same information in a different visual form.
Key Facts
- A dot plot shows each data value as one dot placed above its position on a number line.
- In a stem-and-leaf plot, value = 10 x stem + leaf for two-digit whole numbers.
- The leaves in each row should be written in ascending order.
- Frequency =
- Range =
- For small data sets, both dot plots and stem-and-leaf plots preserve the original data values.
Vocabulary
- dot plot
- A graph that shows each data value as a dot above a number line.
- stem-and-leaf plot
- A table-like display that separates each number into a stem and a leaf to keep values ordered.
- frequency
- The frequency of a value is the number of times it appears in a data set.
- distribution
- The distribution describes how data values are spread out across possible values.
- outlier
- An outlier is a value that is much larger or much smaller than most of the other data.
Common Mistakes to Avoid
- Placing dots between tick marks on a dot plot, which is wrong because each dot must sit exactly above its actual data value on the number line.
- Writing stem-and-leaf leaves out of order, which is wrong because unordered leaves make the data harder to read and can hide the true shape of the distribution.
- Using inconsistent place values for stems and leaves, which is wrong because every number in the plot must be split the same way for the display to make sense.
- Forgetting that repeated values need repeated dots or repeated leaves, which is wrong because leaving out duplicates changes the frequencies and misrepresents the data set.
Practice Questions
- 1 A class recorded these quiz scores: 12, 15, 15, 17, 18, 21, 21, 24, 26. Make a dot plot and a stem-and-leaf plot for the data, then find the range.
- 2 The daily temperatures for one week were 63, 65, 65, 66, 68, 70, 72, 72, 72, 74. Create a stem-and-leaf plot using tens as stems and ones as leaves. Then state the frequency of 72 and the range of the data.
- 3 A data set has several repeated values and one unusually large value. Explain how that pattern would appear in a dot plot and in a stem-and-leaf plot.