Histogram Calculator
Create histograms from your data with automatic binning and frequency analysis
Data Input
Enter up to 50 data points. New fields appear automatically as you add data. Valid data points: 0
Example: Dice Roll Results
Sample Data
Scenario: Results from 20 dice rolls
Data: 1, 4, 3, 6, 4, 4, 2, 5, 1, 6, 3, 2, 4, 5, 6, 1, 3, 5, 2, 4
Purpose: Visualize the frequency distribution of dice outcomes
Expected Results
• Each value (1-6) should appear with roughly equal frequency
• Histogram should be approximately uniform
• Total frequency should equal 20 (number of rolls)
• Mean should be around 3.5 (theoretical mean for fair die)
Histogram Shapes
Normal
Bell-shaped, symmetric distribution
Right Skewed
Tail extends to the right
Left Skewed
Tail extends to the left
Uniform
All values have equal frequency
Histogram Tips
Use 5-20 bins for most datasets
Bins should have equal width
Shows data distribution shape
Height represents frequency
Good for continuous data
Reveals outliers and patterns
Understanding Histograms
What is a Histogram?
A histogram is a graphical representation of data that shows the frequency distribution of a dataset. It organizes data into bins (intervals) and displays how many data points fall within each bin.
Key Components
- •Bins: Intervals that group similar values
- •Frequency: Number of data points in each bin
- •Bin Width: Range of values in each bin
- •Height: Represents frequency of each bin
Histogram vs Bar Chart
Histogram
- • Shows frequency distribution
- • Continuous data (numerical)
- • Bars touch each other
- • X-axis shows ranges/intervals
- • Used for quantitative data
Bar Chart
- • Shows comparisons between categories
- • Discrete data (categorical)
- • Bars have gaps between them
- • X-axis shows categories
- • Used for qualitative data
Interpreting Histogram Shapes
Normal Distribution
Bell-shaped curve with most data points clustered around the center (mean).
Example: Heights, test scores, measurement errors
Right Skewed
Long tail on the right side, with most data concentrated on the left.
Example: Income distribution, house prices, waiting times
Left Skewed
Long tail on the left side, with most data concentrated on the right.
Example: Age at retirement, test scores (when most do well)
Choosing the Right Number of Bins
The number of bins significantly affects how your histogram looks:
- • Too few bins: May hide important patterns in the data
- • Too many bins: May create noise and make patterns unclear
- • Sturges' Rule: k = log₂(n) + 1 (where n = sample size)
- • Square Root Rule: k = √n
- • General guideline: 5-20 bins work well for most datasets