Chart Interpretation

How to Write Your Results — 5 Templates

Each card is auto-filled from the live values. Use the 📋 Copy buttons to paste into your paper, thesis, poster, or pre-registration.

Bin-width rules

Sturges:           k = ⌈1 + log₂(n)⌉
Scott:             h = 3.5 · s · n^(−1/3)
Freedman–Diaconis: h = 2 · IQR · n^(−1/3)
Square-root:       k = ⌈√n⌉

Where:
  k   = number of bins
  h   = bin width
  n   = sample size
  s   = sample standard deviation
  IQR = Q3 − Q1
      

KDE bandwidth (Silverman's rule)

bw = 0.9 · min(s, IQR/1.34) · n^(−1/5)

f(x) = (1 / (n · bw)) · Σ K((x − xᵢ) / bw)
K(u) = (1 / √(2π)) · exp(−u²/2)   (Gaussian kernel)
      

Normal curve overlay

For frequency mode the Gaussian density is scaled by n·h to match histogram counts; for density mode the curve uses raw PDF; for relative-frequency mode it is scaled by h.

Libraries

Rendered with Chart.js 4.4.1. CSV/Excel parsing via SheetJS 0.18.5. All computations performed client-side.

1. Choose how to enter data. Three tabs: paste (comma-separated), upload (CSV/Excel with column picker), or manual entry.
2. Edit the variable name. It is reused in axis labels, the legend, the figure caption, and every export.
3. Pick a sample dataset. Five USA-based examples are pre-built. Dataset 1 (Chicago commute) is loaded into the input by default — edit it or paste your own values, then click Generate Plot to render.
4. Choose a bin-width rule. Freedman–Diaconis is the safest default. Scott for near-normal data, Sturges for small samples, Square-root for quick exploration, Custom for a fixed count.
5. Toggle the overlays. Normal curve, KDE density, mean line, median line, ±1 SD band, and per-bar value labels are all independently switchable.
6. Set the Y-axis units. Frequency (count), relative frequency (%), or density — the curves rescale automatically.
7. Edit titles, axes, and caption. Inline fields control every label that appears on the exported image. The big

   at the top of the page is also editable — click and type.

8. Choose fonts and colours. Eight palettes (including Colorblind-safe Okabe–Ito), individual colour pickers for bars/curves/lines/background, opacity slider, font family selector, and per-element size controls.
9. Set canvas size and DPI. Default 900 × 520 px at 2× retina; switch to 3× for print, or 1× for the web.
10. Export. PNG (lossless, journals), JPEG (slides), WebP (web), or TXT (statistics report).

Use a histogram when…

• ✅ Your variable is continuous (interval or ratio).
• ✅ You have at least 20–30 observations (50+ is much better).
• ✅ You want to assess normality before a t-test, ANOVA, or regression.
• ✅ You want to detect skewness, bimodality, or outliers.

Use an alternative when…

• ❌ Your variable is categorical → use a bar chart.
• ❌ You have fewer than 15 observations → use a dot plot or stem-and-leaf.
• ❌ You want to compare 2+ groups → use grouped box plots or violin plots.
• ❌ You want a smooth density estimate → use a KDE (toggle the KDE overlay in this tool).

Decision tree

Numeric variable?
├─ Yes → continuous?
│   ├─ Yes → HISTOGRAM ✓  (this tool)
│   └─ No (discrete count) → bar chart of counts
└─ No (categorical)        → bar chart
      

Real-world USA examples

1. Public health — daily-step distribution for 2,400 Fitbit users in California.
2. Education — SAT Math score distribution across a Los Angeles high-school district.
3. Real estate — single-family home prices in Atlanta showing a long right tail driven by luxury sales.