Organizing Quantitative Data
Numbers tell stories. Learn how to visualize numerical data through histograms, stem-and-leaf plots, and dot plots—and recognize the shapes they form.
Discrete Data Displays
Discrete Histograms
When discrete data has few distinct values (e.g., number of children: 0, 1, 2, 3...), the categories ARE the observations themselves.
- • Bars are centered over the discrete value
- • Bars touch each other (unlike qualitative bar graphs)
- • Height = Frequency of that specific value
Touching bars show the underlying numerical nature of the data. Even though "2 children" and "3 children" are distinct counts, they're connected on the number line—unlike "Red" and "Blue" which have no numerical relationship.
Interactive Discrete Histogram Tool
Enter discrete data values (whole numbers) to automatically generate a frequency table and histogram. Bars will touch to show the numerical relationship between values.
Enter data values above or select a sample dataset to get started.
Continuous Data & Classes
The smallest value that can belong to a class
The largest value that can belong to a class
Difference between consecutive lower limits
(Round UP to a convenient number)
Classes like 10–19, 20–29, 30–39 are correct. Classes like 10–20, 20–30 would cause confusion (where does 20 go?).
Continuous Histogram & Class Width Calculator
Enter continuous data values to calculate class width, generate a frequency distribution table, and visualize with a histogram. Adjust the number of classes or set a custom class width.
Enter data values above or select a sample dataset to get started.
Stem-and-Leaf Plots
Construction
Stem: All digits to the LEFT of the rightmost digit
Leaf: The rightmost digit only
Unlike histograms that group data into bins, stem-and-leaf plots let you see the distribution shape while retaining every original data value. You can reconstruct all raw data from the plot!
Back-to-Back Stem-and-Leaf Plot
Used to compare two data sets. The stem is shared in the middle, with leaves extending left for one group and right for another.
Reading: Class A scored 65, 68, 69... | Class B scored 62, 64, 67...
- • Quickly see which group has higher or lower values
- • Compare the spread of each distribution at a glance
- • Identify if one group is skewed differently than the other
- • Note: Left-side leaves are read right-to-left (closest to stem first)
Interactive Stem-and-Leaf Plot Tool
Enter data values (0-99) to create a stem-and-leaf plot. The stem is the tens digit, the leaf is the units digit.
Enter data values above or select a sample dataset to get started.
Dot Plots
Simple & Powerful
A number line where each observation is represented by a dot placed above its corresponding value. Multiple observations at the same value stack vertically.
Reading: Value "1" appears 2 times, Value "2" appears 2 times, etc.
Interactive Dot Plot Tool
Enter data values to create a dot plot. Each dot represents one observation, stacked vertically when values repeat.
Enter data values above or select a sample dataset to get started.
Identifying Distribution Shapes
Uniform
Frequencies are roughly equal across all values. Flat, rectangular shape.
Examples: Rolling a fair die, random number generators
Bell-Shaped (Symmetric)
Highest frequency in the middle, tapering off symmetrically on both sides.
Examples: IQ scores, heights, SAT scores
Skewed Right
The right "tail" is longer. Most data clusters on the left.
Examples: Income distribution, home prices, wait times
Skewed Left
The left "tail" is longer. Most data clusters on the right.
Examples: Age at retirement, exam scores (easy test), death ages
The direction of the longer tail tells you the skew direction. Tail points right → Skewed Right. Tail points left → Skewed Left.