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Quartile Calculator (Q1, Q3, IQR)

Get the five-number summary of any data set: min, Q1, median, Q3 and max, plus the interquartile range and 1.5×IQR outlier fences with flagged outliers.

Enter at least 3 numbers to compute the five-number summary, IQR and outlier fences.

What is the Quartile Calculator (Q1, Q3, IQR)?

The ByteTools Quartile Calculator sorts your data and returns the five-number summary — minimum, first quartile (Q1), median, third quartile (Q3) and maximum — along with the interquartile range (IQR = Q3 − Q1).

  • Five-number summary: min, Q1, median, Q3, max
  • Interquartile range (IQR) and quartile deviation
  • 1.5 × IQR outlier fences with flagged outliers listed
  • Median-of-halves quartile method, as taught in most courses
  • Shows the sorted data set for easy verification
  • 100% private — everything computed in your browser

How to use the Quartile Calculator (Q1, Q3, IQR)

  1. 1

    Paste your numbers, separated by commas, spaces or new lines.

  2. 2

    Read the five-number summary: min, Q1, median, Q3 and max.

  3. 3

    Check the interquartile range (IQR) and the lower and upper fences.

  4. 4

    Review any values flagged as outliers by the 1.5 × IQR rule.

  5. 5

    Copy the full summary with one click.

About the Quartile Calculator (Q1, Q3, IQR)

The ByteTools Quartile Calculator sorts your data and returns the five-number summary — minimum, first quartile (Q1), median, third quartile (Q3) and maximum — along with the interquartile range (IQR = Q3 − Q1). Quartiles are computed with the median-of-halves (Tukey exclusive) method used in most statistics courses.

It goes a step further and computes the standard 1.5 × IQR outlier fences: any value below Q1 − 1.5×IQR or above Q3 + 1.5×IQR is flagged and listed as a potential outlier — exactly the rule used to draw box-plot whiskers. That makes the tool a fast sanity check before deeper analysis.

Your numbers are processed 100% locally in your browser and never uploaded, so the calculator is private, instant and works offline. Paste data straight from a spreadsheet column and read off the summary.

Frequently asked questions

How do you find Q1 and Q3?

Sort the data and find the median. Q1 is the median of the lower half and Q3 is the median of the upper half; with an odd count, the overall median is excluded from both halves. For 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49 the median is 40, Q1 = 15 and Q3 = 43.

What is the interquartile range used for?

The IQR measures the spread of the middle 50% of the data, so unlike the full range it is not distorted by a single extreme value. It is the box width in a box plot and the basis of the most common outlier rule.

How does the 1.5 × IQR outlier rule work?

Compute the fences: Q1 − 1.5×IQR and Q3 + 1.5×IQR. Any observation outside these fences is a potential outlier. It is a screening rule rather than proof of a bad data point — flagged values deserve investigation, not automatic deletion.

Why does my calculator give slightly different quartiles?

There are several legitimate quartile conventions. This tool uses the median-of-halves (exclusive) method common in textbooks and TI calculators; Excel's QUARTILE.INC interpolates differently and can give slightly different Q1/Q3 for small data sets. Both are correct under their own definitions.

What is the five-number summary?

It is the minimum, Q1, median, Q3 and maximum — five values that sketch the whole distribution: its centre, spread and range. It is exactly the information a box-and-whisker plot displays graphically.

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