Histogram Calculator
Generate histogram bin frequencies and visualization from raw data and bin width. Enter values for instant results with step-by-step formulas.
Formula
Bin width = Range / k; Frequency = count per bin; Density = relative frequency / bin width
Where k is the number of bins, Range = max - min, relative frequency = count/n. Sturges rule: k = ceil(log2(n) + 1). Scott rule: h = 3.49 * s * n^(-1/3). Rice rule: k = ceil(2 * n^(1/3)).
Worked Examples
Example 1: Exam Score Distribution
Problem: Analyze the distribution of 20 exam scores: 55, 60, 62, 65, 68, 70, 72, 74, 75, 76, 78, 80, 82, 84, 85, 88, 90, 92, 95, 98 using Sturges rule.
Solution: n = 20, Range = 98 - 55 = 43\nSturges bins = ceil(log2(20) + 1) = ceil(4.32 + 1) = ceil(5.32) = 6\nBin width = 43 / 6 = 7.17\nBins: [55-62.2]: 3, [62.2-69.3]: 2, [69.3-76.5]: 5, [76.5-83.7]: 3, [83.7-90.8]: 3, [90.8-98]: 4\nMode bin: [69.3-76.5] with 5 observations
Result: 6 bins | Bin width = 7.17 | Mode bin: 69.3-76.5 (25% of data)
Example 2: Manufacturing Quality Control
Problem: Widget weights (grams): 9.8, 9.9, 10.0, 10.0, 10.1, 10.1, 10.1, 10.2, 10.2, 10.3, 10.3, 10.4, 10.5, 10.6, 10.8. Create a 5-bin histogram.
Solution: n = 15, Range = 10.8 - 9.8 = 1.0\nBin width = 1.0 / 5 = 0.20\nBins: [9.8-10.0]: 2, [10.0-10.2]: 5, [10.2-10.4]: 4, [10.4-10.6]: 2, [10.6-10.8]: 2\nMean = 10.22, Std Dev = 0.267\nMost data concentrated in 10.0-10.4 range (60%)
Result: 5 bins | Mode bin: 10.0-10.2 (33%) | Mean = 10.22g | StdDev = 0.267g
Frequently Asked Questions
What is a histogram and what does it show?
A histogram is a graphical representation of the distribution of numerical data using rectangular bars. Each bar spans a range of values (called a bin or class interval) and its height represents the number of data points (frequency) that fall within that range. Unlike a bar chart, histograms display continuous data with no gaps between bars, emphasizing that the data is continuous. Histograms reveal the shape of a distribution, including its center, spread, skewness, and the presence of multiple modes or peaks. They are essential tools in exploratory data analysis, quality control, and any situation where understanding the distributional properties of a dataset is important.
How do you choose the right number of bins for a histogram?
Choosing the right number of bins involves balancing detail against noise. Too few bins oversimplify the distribution and hide important features. Too many bins create a jagged, noisy picture with random spikes. Several mathematical rules provide guidance. The Sturges rule uses k = 1 + log2(n), which works well for roughly normal data up to a few hundred observations. The Scott rule sets bin width as h = 3.49 * s * n^(-1/3) based on standard deviation, optimizing for normal distributions. The Rice rule uses k = 2 * n^(1/3), which often gives more bins than Sturges. The Freedman-Diaconis rule uses h = 2 * IQR * n^(-1/3), which is more robust to outliers. In practice, try several values and see which best reveals the data structure.
How do you identify the shape of a distribution from a histogram?
Distribution shapes have standard descriptions. A symmetric or bell-shaped histogram has roughly equal tails on both sides and a single central peak, suggesting a normal distribution. A right-skewed (positively skewed) histogram has a longer tail extending to the right, common in income, housing prices, and reaction times. A left-skewed (negatively skewed) histogram has a longer tail to the left, seen in age at retirement or easy exam scores. A bimodal histogram has two distinct peaks, suggesting two subpopulations (like heights of mixed-gender groups). A uniform histogram has roughly equal bar heights across all bins. Identifying the shape guides the choice of appropriate statistical methods and summary measures.
Can I use Histogram Calculator on a mobile device?
Yes. All calculators on NovaCalculator are fully responsive and work on smartphones, tablets, and desktops. The layout adapts automatically to your screen size.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
How do I get the most accurate result?
Enter values as precisely as possible using the correct units for each field. Check that you have selected the right unit (e.g. kilograms vs pounds, meters vs feet) before calculating. Rounding inputs early can reduce output precision.