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

N

Normal

Bell-shaped, symmetric distribution

R

Right Skewed

Tail extends to the right

L

Left Skewed

Tail extends to the left

U

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