Five-number summary calculator
For 1, 3, 5, 7, 9, 11 and 13 you get a minimum of 1, Q1 of 3, a median of 7, Q3 of 11 and a maximum of 13: the five landmarks of a box plot, with no normal shape assumed. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- Data
- 1, 3, 5, 7, 9, 11, 13
- N
- 7
- Min
- 1
- Q1
- 3
- Median
- 7
The five-number summary is the classic compact portrait of a numeric sample: the minimum, the first quartile, the median, the third quartile, and the maximum. Together these five landmarks describe where the data starts, where the middle half sits, and where the extremes land, without assuming a normal shape or computing a mean that outliers can drag. Teachers draw box plots from exactly these hinges; analysts scan them before deeper modeling; quality teams glance at them when a process column drifts. An empty list is rejected with a clear validation error, because every five-number summary needs at least one observation.
How the five-number summary is computed
Begin with a non-empty collection of finite real numbers. Copy the list and sort it in non-decreasing order so every later step is order-statistic arithmetic rather than a scan that depends on input order. The minimum is the first sorted value and the maximum is the last; those two bookends are unambiguous for any sample size.
The median is the middle value when the count n is odd, or the arithmetic mean of the two central values when n is even, matching the definition students meet in introductory statistics.
The first and third quartiles use Tukey hinges: form the lower half as the first floor of n over two observations and the upper half as the last floor of n over two observations, deliberately excluding the overall median when n is odd so the hinge is the median of the lower or upper cloud rather than a percentile interpolation formula that varies by software. Q1 is then the median of the lower half and Q3 the median of the upper half.
When n equals one, every hinge collapses to that single observation so the summary is still well defined. The interquartile range is Q3 minus Q1 and measures the spread of the central half of the data, which is more resistant to extreme outliers than a standard deviation. Empty lists, non-numeric tokens, NaN, and Infinity are rejected with invalid input instead of inventing fake hinges.
Where five-number summaries show up in real work
Exploratory data analysis starts with these five hinges before anyone fits a model, because they reveal location, spread, and possible outliers without assuming normality. Quality control and process monitoring teams track min, median, and quartile drift on sensor columns day over day when full distributional models would be overkill. Sports analytics, psychometrics, and operations research summarize season scores, item times, and queue wait lengths with the same five numbers so stakeholders read one shared table.
If you later need z-scores, full CSV column profiles, percentile ranks with a different interpolation type, or mean and standard deviation alone, treat those as separate search intents and landings rather than overloading this five-number summary calculator page.
What you can do with it
Homework and box-plot answer keys
Generate min, Q1, median, Q3, and max for textbook data sets so teachers and auto-graders share one ground truth for box-and-whisker plots.
Quick exploratory data checks
Paste a numeric column and read the five hinges plus IQR before deciding whether to transform, trim outliers, or fit a model.
Process and scoreboard summaries
Summarize sensor readings, exam scores, or queue times with resistant quartiles that extreme spikes do not dominate.
FAQ
What is a five-number summary?
It is the ordered set of minimum, first quartile (Q1), median, third quartile (Q3), and maximum for a numeric sample. Those five values describe location and spread and are the hinges used to draw a box plot.
How are Q1 and Q3 calculated here?
With Tukey hinges: after sorting, Q1 is the median of the lower half (first floor(n/2) values) and Q3 is the median of the upper half (last floor(n/2) values). When n is odd the overall median is excluded from both halves.
What happens if the list is empty?
A five-number summary is undefined for zero observations; provide at least one finite number.
Does the order of my numbers matter?
No. The calculator sorts a copy ascending before computing hinges, so any permutation of the same values yields the same summary.
What does it cost?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/stat/five-number-summary \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"data":"1, 3, 5, 7, 9, 11, 13"}'const res = await fetch("https://api.kit.forhosting.com/stat/five-number-summary", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"data": "1, 3, 5, 7, 9, 11, 13"
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/five-number-summary",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"data": "1, 3, 5, 7, 9, 11, 13"
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/five-number-summary", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"data":"1, 3, 5, 7, 9, 11, 13"}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"data":"1, 3, 5, 7, 9, 11, 13"}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/five-number-summary", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"data": "1, 3, 5, 7, 9, 11, 13"
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.five_number_summary",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
This calculator accepts a list of finite numbers as a JSON array or a comma, space, or semicolon separated string, sorts a copy ascending, and returns Tukey hinges: the overall median, plus the medians of the lower and upper halves for Q1 and Q3.
How the five-number summary is computed
The entire pipeline is deterministic floating-point math with no random seeds, no wall-clock timestamps, and no network calls, so identical inputs always produce identical JSON.
What you send and what you get back
Provide exactly one of those three field names. Classic textbook checks include the odd sample one, three, five, seven, nine, eleven, thirteen, whose median is seven and whose halves give Q1 equals three and Q3 equals eleven, and even samples such as two, four, six, eight where the median averages the two central values. Send one required field named data, or the aliases values or numbers, holding either a JSON array of finite numbers or a plain string with numbers separated by commas, spaces, or semicolons. Missing fields, empty arrays, empty strings, non-numeric tokens, NaN, and Infinity fail with invalid_input and are not charged. On success the response echoes the count n, the sorted cleaned values, scalar fields min, q1, median, q3, and max, the interquartile range iqr, a compact five_number_summary array in the traditional order minimum then Q1 then median then Q3 then maximum, the method label tukey_hinges, and a short formula string. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance. Because the engine is pure parse code, latency stays sub-millisecond for ordinary classroom lists and modest API payloads.
Where five-number summaries show up in real work
Secondary-school and college statistics courses constantly assign five-number drills, box-and-whisker constructions, and comparisons of skewed versus symmetric samples; a single trusted oracle that returns cleaned JSON speeds grading and demo setup. Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.