Insyt
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Distribution

Notched box plot

Adds notches to approximate uncertainty around the median.

  • Plot
  • Distribution
  • Uncertainty

What it answers

How uncertain is the estimated median?

Shape
Box indented around its median
What it shows
Approximate median uncertainty.

Example

The question

Is the median delivery time really different between two carriers?

Days to deliver by carrier, with notches around the median (illustrative)

Days to deliver by carrier, with notches around the median (illustrative)Notches show the uncertainty around each median; they do not overlap, so the medians likely differ. Carrier A: median 4.2, middle half 3.6 to 5, range 1 to 6.9; Carrier B: median 5.3, middle half 4.2 to 6.2, range 2.1 to 9.8.Days to deliver0246810Carrier ACarrier B
Days to deliver by carrier, with notches around the median (illustrative)Notches show the uncertainty around each median; they do not overlap, so the medians likely differ. Carrier A: median 4.2, middle half 3.6 to 5, range 1 to 6.9; Carrier B: median 5.3, middle half 4.2 to 6.2, range 2.1 to 9.8.Days to deliver0246810Carrier ACarrier B
Notches show the uncertainty around each median; they do not overlap, so the medians likely differ. Carrier A: median 4.2, middle half 3.6 to 5, range 1 to 6.9; Carrier B: median 5.3, middle half 4.2 to 6.2, range 2.1 to 9.8.

Illustrative data. It belongs to no company.

When to use it

Use it when

Exploratory comparison of medians with adequate data.

Avoid it when

Small samples or interpreting notch overlap as a universal significance test.

How to read it

Read the median line and notch extent, with the calculation explained.

Note

Notch calculations differ across implementations.

The data you need

Layout
Long table
Fields
Group: text; Value: number
One row is
One raw observation belonging to a group. What is the grain?
Rules
Retain individual observations and group labels. State weighting and missing-data rules.
Optional
For box plots only, some tools accept Group,Q1,Median,Q3,WhiskerLow,WhiskerHigh plus separate outliers. Other distributions usually need raw data.
Preparation
Keep raw numeric observations, group them if needed and handle missingness explicitly. Choose bins, bandwidth or summary conventions as appropriate to this specific plot.
Units
The measurement axis retains its original unit. Frequency uses observations; normalised frequency divides by group sample size; density also depends on interval width.
Example of the input layout: Long tableA long table: one row per observation, few columns. New data adds rows.GroupValueAABBC
A long table: one row per observation, few columns. New data adds rows.

Worked example

Suppose precomputed median 10, notch 9-11, Q1=8, Q3=13. Draw these supplied summaries. The notch describes estimated median uncertainty.

GroupValue
A10
A12
A18
B11
B23
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