Frequency Distribution Calculator
Build a frequency distribution table from data. Calculate relative and cumulative frequencies.
What Is the Frequency Distribution Calculator?
The Frequency Distribution Calculator organizes raw data into a frequency table with class intervals, frequencies, relative frequencies, and cumulative frequencies. It helps visualize how data is distributed across ranges and is the first step in statistical data analysis.
Formula
How to Use
Enter your raw data values separated by commas. Choose the number of classes (bins) or let the tool determine the optimal number using Sturges' rule (k ≈ 1 + 3.322·log₁₀(n)). The calculator creates a frequency table with class boundaries, midpoints, frequencies, and relative frequencies.
Example Calculation
Data: 45, 52, 61, 48, 55, 67, 70, 53, 59, 72. n=10, range=72−45=27, k=4 classes, width=7. Classes: [45,52): 2, [52,59): 3, [59,66): 2, [66,73): 3. Relative: 0.2, 0.3, 0.2, 0.3.
Understanding Frequency Distribution
A frequency distribution organizes a large collection of raw data values into a compact table showing how often values fall in each class interval. This transformation reveals the shape, center, and spread of the data at a glance — turning a meaningless list of numbers into an interpretable statistical summary.
The choice of class width and number of classes significantly affects the appearance of the distribution. Sturges' rule provides a starting point, but analysts often adjust the number of bins based on the data's range, sample size, and the question being asked. Class boundaries should be chosen to avoid ambiguity — half-integer boundaries (e.g., 9.5, 19.5) are a common solution.
Frequency distributions are the foundation of descriptive statistics and the basis for constructing histograms, frequency polygons, and ogive (cumulative frequency) curves. They are used in quality control (Pareto analysis), demography (age distribution), meteorology (rainfall frequency), and every field where understanding the distribution of measurements matters.
Frequently Asked Questions
How many classes should a frequency distribution have?
Typically 5 to 20 classes. Sturges' rule suggests k = 1 + 3.322·log₁₀(n). Too few classes hide the distribution shape; too many create sparse, noisy bins.
What is relative frequency?
Relative frequency is the proportion of observations in each class: relative frequency = class frequency / total number of observations. It expresses frequency as a fraction (or percentage).
What is cumulative frequency?
Cumulative frequency is the running total of frequencies up to and including each class. The last cumulative frequency always equals n (total observations).
What distribution shapes can I identify from a frequency table?
Bell-shaped (normal), skewed left or right, uniform, bimodal, or J-shaped distributions. Histograms (bar charts of frequency distributions) make these shapes visually apparent.
Is this calculator free?
Yes, completely free with no sign-up needed.