HesapHanem

Five Number Summary Calculator

Find the five-number summary of any data set

Result

Min 2.00, Q1 4.50, Median 9.00, Q3 13.50, Max 18.00
9.00

How it is calculated

The tool reads the numbers you type (separated by commas, semicolons, spaces or line breaks), silently drops anything that is not a number, and sorts the rest. The minimum and maximum are the first and last values. The median is the middle value, or the mean of the two middle values when the count n is even. Q1 is the median of the lower ⌊n/2⌋ values and Q3 the median of the upper ⌊n/2⌋ values. When n is odd, the overall median is left out of both halves. The interquartile range is IQR = Q3 − Q1.

At least two valid numbers are needed. Other software (spreadsheets, calculators) may use inclusive or interpolated quartiles and give slightly different Q1 and Q3 for the same data. Results are shown to two decimals.

Worked example

Data: 12, 5, 9, 2, 18, 4, 15, 7, 10. Sorted: 2, 4, 5, 7, 9, 10, 12, 15, 18, so n = 9. The median is the 5th value, 9. Lower half (without the median): 2, 4, 5, 7, whose median is (4 + 5) / 2 = 4.5. Upper half: 10, 12, 15, 18, whose median is (12 + 15) / 2 = 13.5. The tool shows Min 2.00, Q1 4.50, Median 9.00, Q3 13.50, Max 18.00 and an IQR of 13.5 − 4.5 = 9.00.

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Common mistakes

  • Typing a decimal comma such as 2,5. Commas split values, so 2,5 is read as two numbers, 2 and 5. Use a decimal point.
  • Expecting the odd-n median to count in both halves. This tool excludes it; software using the inclusive method will report a different Q1 and Q3.
  • Not noticing that non-numeric entries are skipped. A typo like 1O (letter O) is dropped without a warning, changing n and the quartiles.
  • Calculating quartiles on unsorted data by hand. The tool sorts for you, but a manual check must sort first.
  • Treating the IQR as the full spread. The range is Max − Min; the IQR covers only the middle half of the data.

About this calculator

This calculator computes the classic five-number summary — minimum, Q1, median, Q3, maximum — using the exclusive quartile method: find the overall median, then split the data into a lower and upper half (excluding the median itself when n is odd), and take the median of each half as Q1 and Q3 respectively.

Statisticians and data analysts use this summary as the backbone of a box-and-whisker plot and as a fast way to eyeball a distribution's center, spread, and skew without computing a full set of descriptive statistics — it's also the standard starting point for flagging outliers via the interquartile range (Q3 − Q1).

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Comments (1)

  • Editorial team

    The tool does not flag outliers, but the numbers it shows make the usual test easy. A value above Q3 + 1.5 × IQR or below Q1 − 1.5 × IQR is a candidate. For 3, 5, 6, 7, 8, 9, 10, 40, Q3 is 9.50 and the IQR is 4.00, so the upper fence is 15.50 and 40 stands out. Does your course or software use inclusive quartiles? Tell us which method you need.

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