Your result
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Enter your values, then click Calculate result.How this calculator helps
A five number summary calculator condenses the position and spread of observed data into five ordered values. It answers a different question from the mean and standard deviation: where are the endpoints, central observation and quarter boundaries? Use it for a classroom data list, a distribution comparison or the numerical ingredients of a box plot. No observations are generated or removed to improve the appearance of the distribution.
How to use it
- 1
Paste the observed numeric list and retain repeated observations.
- 2
Choose whether the odd central median belongs in the lower and upper halves.
- 3
Click Calculate result and read the five ordered values, IQR and count.
- 4
Record the quartile convention; compare any box-plot whiskers separately from the actual endpoints.
Formula and methodology
Sort observations. Minimum and maximum are endpoints. Q2 is the median. Q1 and Q3 are medians of the chosen lower and upper halves. IQR = Q3 − Q1.
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
For 1, 2, 3, 4, 5, exclusive halves give Q1 = 1.5, median = 3 and Q3 = 4.5. The five-number summary is 1, 1.5, 3, 4.5, 5 and IQR is 3. Inclusive halves give Q1 = 2 and Q3 = 4. The data have not changed; the quartile convention has. This example makes a software disagreement visible rather than treating one program as automatically wrong.
How to interpret your result
Read the result in the order minimum, Q1, median, Q3, maximum. The sequence must be nondecreasing. A wide central interval indicates spread in the middle half under the selected convention, while a large endpoint gap may reflect a tail. Neither pattern identifies a cause. To compare classes or batches fairly, use the same units, sampling rules and quartile method.
For different inputs or formulas, use Mean Standard Deviation Calculator; Stem And Leaf Plot Generator; Z Score Calculator.
Related questions this calculator covers
- five number summary calculator
- 5 number summary calculator
Scenario comparison
| Scenario | What it shows |
|---|---|
| Odd count | 1,2,3,4,5 changes quartiles when the median convention changes. |
| Even count | 1,2,3,4 has median 2.5 and half-medians 1.5 and 3.5. |
| Constant data | 7,7,7 gives a zero IQR and all endpoints equal to 7. |
Common mistakes to avoid
- Removing repeated observations before sorting.
- Comparing half-medians with a spreadsheet percentile interpolation without noting the method.
- Treating a value beyond an IQR fence as automatically invalid.
Sort a short sample by hand, identify its central position and form the lower and upper halves under the chosen rule. Calculate the median of each half independently. Check that minimum ≤ Q1 ≤ median ≤ Q3 ≤ maximum. Add a constant to all values and verify that each endpoint shifts by that constant while IQR remains unchanged.
Authoritative reference. Method reference checked for this worksheet. The calculation and examples are independently implemented; read the specific scope and units above.What can affect the result?
Choose the quartile convention
For an odd number of observations, excluding the central median leaves equal halves without that central value. Including it places the median in both halves. For an even count, both options use the same equal halves. These are median-of-halves conventions, not every percentile algorithm used by spreadsheets. State the convention with any exported summary so another person can reproduce the calculation from the same list.
Sort observations without losing frequency
Every repeated value is a separate observation and remains in the sorted list. A data set with values 2, 2, 2, 8 differs from 2, 8 because the frequencies are different. Commas, spaces, semicolons and newlines are separators. Use a decimal point inside a number; a comma is not interpreted as a thousands separator or a decimal-comma locale marker. Labels and missing-value codes are rejected.
Understand the interquartile range
The IQR describes the separation between Q1 and Q3 in the original measurement units. It is not a percentage and does not require a normal distribution. Two lists can share a median while having very different IQRs. Adding the same constant to every observation shifts all five summary values but leaves IQR unchanged. Multiplying every observation by a positive factor scales both the summary and IQR by that factor.
Fences are screening references
Lower and upper fences are Q1 minus 1.5 IQR and Q3 plus 1.5 IQR. A value beyond a fence is a candidate for inspection under this rule, not proof of a recording error. Maximum and minimum remain the actual endpoints even when they lie beyond the fences. The tool does not silently replace them with whisker endpoints or delete outliers. A box-plot program may draw whiskers differently.
Small samples and constant lists
A single observation is returned as all five summary values because no independent spread is available. For a constant list, IQR is zero and both fences equal that shared value. These edge cases are useful arithmetic checks but do not establish population variability. With a small sample, one added observation can change a half-median substantially. Keep the count next to the summary when comparing data collections.
Precision and input limits
The browser accepts up to 1,000 finite observations within the disclosed numerical bounds. It uses ordinary floating-point numbers, so displayed decimals should not be interpreted as measurement certainty. A five-value summary cannot reveal every cluster, gap or ordering pattern in the original list. Preserve the original observations for a histogram or stem-and-leaf inspection instead of relying on the summary alone.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
Use only the disclosed input domains and model. Removing repeated observations before sorting. Review the method-specific boundaries above and the linked source before interpreting a result. Calculations use browser floating-point arithmetic; displayed digits are not a measure of real-world certainty. Your entries stay on this device and are not submitted to a calculation server.
Sources and review information
Frequently asked questions
Why do two calculators give different quartiles?＋
They may use different percentile or half-median conventions. Compare the method and sample size before comparing Q1 and Q3.
Is the median the average?＋
The median is the middle of the sorted list. An arithmetic mean adds all values and divides by their count, so it can differ substantially.
Are the fences the minimum and maximum?＋
No. Fences are calculated screening thresholds. This worksheet retains the observed minimum and maximum even outside those thresholds.
Can I enter negative observations?＋
Yes. Finite signed numbers are supported. The sorted order, not their sign, determines their position in the summary.
Does this draw a box plot?＋
It supplies the numerical summary and IQR fences. It does not draw a graphical box plot or choose a separate whisker convention.