DESCRIPTIVEDescriptive StatisticsStatistics Calculator
📊

Histogram — Visualize Data Distribution

Paste raw data, choose binning method (Sturges, Scott, Freedman-Diaconis), toggle density mode and normal overlay. Get descriptive stats and cumulative histogram.

Concept Fundamentals
8
Bins
100
n
72.40
Mean
Build HistogramMultiple binning methods

Why This Statistical Analysis Matters

Why: Histograms reveal shape, center, spread, and outliers. The right bin count matters — too few bins hide detail; too many create noise.

How: Enter data (comma/space separated). Choose binning: Sturges (classic), Scott (normal-optimal), Freedman-Diaconis (robust). Toggle density for area=1 overlay.

  • ●Sturges: 1+log2(n)
  • ●Scott: optimal for normal
  • ●F-D: robust to outliers
Sources:NIST Engineering StatisticsWikipedia Histogram
📊
DESCRIPTIVE STATISTICSCustomizable histograms

Customizable Histograms — Multiple Binning Methods & Normal Overlay

Paste raw data, choose binning method, toggle density mode and normal overlay. Get descriptive stats and cumulative histogram.

Box Plot →Normal Distribution →

Real-World Scenarios — Click to Load

Data Input

100 values parsed

histogram_results.sh
CALCULATED
n
100
Mean
72.4000
Median
72.5000
SD
13.9095
Skewness
-0.0336
Kurtosis
-1.0140
Shape: Approximately symmetric
Share:
Histogram Result
n = 100 · 8 bins
μ = 72.40 · σ = 13.91
Skewness: -0.03Kurtosis: -1.01Bin width: 7.0000
numbervibe.com/calculators/statistics/histogram-calculator

Histogram (Frequency) — 8 bins, width = 7.0000 + Normal N(μ,σ) overlay

Normal Curve Overlay (N(μ,σ))

Cumulative Histogram

Bin Frequency Table

BinFrequencyRelative
44.00 – 51.0066.00%
51.00 – 58.001111.00%
58.00 – 65.001515.00%
65.00 – 72.001616.00%
72.00 – 79.001515.00%
79.00 – 86.001616.00%
86.00 – 93.001414.00%
93.00 – 100.0077.00%

Calculation Breakdown

COMPUTATION
Sample size n
100
Range
56.0000
Max − Min = 100 − 44
Binning method
sturges
k = ⌈1 + log₂(n)⌉
Number of bins k
8
Bin width
7.0000
Range/k = 56.00/8
NORMAL OVERLAY
Mean μ
72.4000
SD σ
13.9095
ext{Sample} ext{standard} ext{deviation}
SHAPE
Skewness
-0.0336
Symmetric

For educational and informational purposes only. Verify with a qualified professional.

📈 Statistical Insights

Sturges

k = ceil(1 + log2(n)) — classic bin count

— 1926

Scott's

Width = 3.49σn^(-1/3) — optimal for normal

— 1979

F-D

Width = 2×IQR×n^(-1/3) — robust

— 1981

Key Takeaways

  • • A histogram displays the distribution of numerical data by grouping values into bins
  • • Density histogram: height = relative frequency / bin width — area sums to 1, comparable to PDFs
  • • Binning methods: Sturges, Scott, Freedman-Diaconis, Rice, Square Root — each has trade-offs
  • • Normal overlay N(μ, σ) helps assess whether data is approximately normal
  • • Skewness > 0.5: right-skewed; < -0.5: left-skewed; near 0: symmetric

Did You Know?

📐Sturges' formula (1926) assumes data can be grouped in powers of 2. For continuous data, it often produces too few bins.Source: Sturges 1926
📊Scott's rule minimizes asymptotic mean integrated squared error when the underlying distribution is normal.Source: Scott 1979
🛡️Freedman-Diaconis uses IQR — robust to outliers. A single extreme value won't distort bin width like SD would.Source: Freedman & Diaconis 1981
📈A density histogram has area = 1, so you can overlay a probability density function (e.g., normal) for comparison.Source: NIST Handbook
🎯Skewness measures asymmetry. Positive = long right tail (income); negative = long left tail.Source: Khan Academy
📉Kurtosis measures tail heaviness. Excess kurtosis &gt; 0: heavier tails than normal; &lt; 0: lighter tails.Source: Wolfram MathWorld

Expert Tips

Normal Data

Use Scott's rule. Density + normal overlay to check normality.

Skewed or Outliers

Use Freedman-Diaconis. IQR is robust.

Too Many Bins

Jagged, noisy histogram. Try fewer bins or a different method.

Too Few Bins

Oversmoothed, hides bimodality. Try Rice or Square Root for more bins.

Binning Methods Comparison

MethodFormulaBest For
Sturges'k = ⌈1 + log₂(n)⌉Classic, small n
Scott'swidth = 3.49σn⁻¹/³Normal data
Freedman-Diaconiswidth = 2×IQR×n⁻¹/³Skewed, outliers
Ricek = ⌈2n¹/³⌉More bins
Square Rootk = ⌈√n⌉Simple heuristic

Frequently Asked Questions

What is a density histogram?

Height = relative frequency / bin width. Total area = 1, so you can overlay probability density functions (e.g., normal) for comparison.

When should I use Scott's vs Freedman-Diaconis?

Scott's for normal/symmetric data. Freedman-Diaconis for skewed data or when outliers are present (uses IQR).

What does skewness mean?

Skewness > 0: right tail longer (e.g., income). Skewness < 0: left tail longer. Near 0: symmetric.

How do I interpret the normal overlay?

If the histogram bars roughly follow the red normal curve, the data may be approximately normal. Large deviations suggest non-normality.

What is kurtosis?

Measures tail heaviness. Excess kurtosis > 0: heavier tails than normal. < 0: lighter tails.

Can I use custom bin count?

Yes. Select Custom and enter your desired number of bins. The calculator will compute equal-width bins.

Binning Rules at a Glance

Sturges
1 + log₂(n)
Scott
3.49σn⁻¹/³
FD
2×IQR×n⁻¹/³
Rice
2n¹/³

Disclaimer: This calculator provides histograms for educational and exploratory data analysis. The best bin width depends on your data and purpose. For publication, consider trying multiple methods and reporting the one that best represents your data.

👈 START HERE
⬅️Jump in and explore the concept!
AI

Related Calculators

Class Width Calculator

Calculate optimal class width for histograms using Sturges', Scott's, Freedman-Diaconis, Rice, and Square Root rules.

Statistics

Skewness Calculator

Computes skewness of a dataset using Fisher-Pearson, Pearson's First/Second, and Bowley methods. Shows how data deviates from symmetry.

Statistics

Descriptive Statistics Calculator

All-in-one: mean, median, mode, range, variance, SD, SEM, CV, skewness, kurtosis, quartiles, IQR, percentiles, min, max, count, sum. The comprehensive...

Statistics

Frequency Polygon Calculator

Create frequency polygons from grouped data. Plots midpoints vs frequencies. Supports overlaying multiple datasets for comparison. Raw data or frequency...

Statistics

Mean Absolute Deviation Calculator

Compute MAD = Σ|xᵢ - x̄|/n from data. Compare MAD about the mean vs MAD about the median. See relationship to standard deviation.

Statistics

Median Absolute Deviation Calculator

Compute MAD = median(|xᵢ − median|). Robust spread measure. Normalized MAD, modified Z-scores, outlier detection (Iglewicz-Hoaglin).

Statistics