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Five-Number Summary Calculator

Find the smallest value, first quartile, median, third quartile, largest value and interquartile range of a list of numbers.

Level: Grade 6

  • Common Core standard 6.SP.B.5.cGiving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
Printable worksheet

Five-Number Summary Calculator

Inputs

Separate with commas, spaces, or new lines. Don't use thousands separators.

Quartile method

Result

Five-number summary (min, Q1, median, Q3, max)

6, 15, 40, 43, 49

For 11 values the five-number summary is 6, 15, 40, 43, 49, with an IQR of 28.

Minimum
6
First quartile (Q1)
15
Median (Q2)
40
Third quartile (Q3)
43
Maximum
49
Interquartile range (IQR)
28
Range
43
Count (n)
11

See the step-by-step solution ↓

Step-by-step solution

  1. Sort the 11 values from smallest to largest, so the middle and quarter points are easy to find

    6, 7, 15, 36, …, 47, 49

  2. The median is the middle value, with half the data on each side

    median=40

  3. Q1, the lower quartile, is the middle of the lower half. The overall median is left out of both halves

    Q1 = median of 6, 7, 15, 36, 39=15

  4. Q3, the upper quartile, is the middle of the upper half

    Q3 = median of 41, 42, 43, 47, 49=43

  5. Find the interquartile range: the distance from Q1 to Q3, which is the spread of the middle half

    IQR=43−15=28

  6. Put the minimum, Q1, median, Q3 and maximum together

    6, 15, 40, 43, 49

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Sum up any list of numbers with five key values. The five-number summary gives the minimum (smallest value), the first quartile (Q1), the median, the third quartile (Q3) and the maximum (largest value). The median is the middle value. Q1 marks the point a quarter of the way up the sorted list, and Q3 marks three quarters of the way up. Together, they show where the data is centered, how spread out the middle half is and how far the extremes reach. They're also the five points drawn in a box plot.

Quartiles don't have one single agreed definition. Different textbooks, calculators and spreadsheets can give different answers for the same data. This calculator lets you choose between the two most common methods, and it tells you which one it used. That way, your answer matches the one you're checking against.

Where it's used

Why this math matters outside the classroom:

  • Box plots. Students draw a box plot of quiz scores from the five numbers 52, 68, 75, 84 and 98.
  • Salary surveys. Salary surveys report the first quartile, median and third quartile so readers see where the middle half of pay falls.
  • Commute times. A city whose commute times have Q1 = 18 and Q3 = 35 minutes has an interquartile range of 17 minutes.
  • Comparing classes. A teacher compares two classes whose medians are both 78 but whose IQRs are 10 and 25 points.
  • Delivery times. A delivery service reports a median of 3 days and a maximum of 9 days to show typical and worst-case waits.

Grade level and standards: Grade 6; Common Core State Standards for Mathematics 6.SP.B.5.c. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Enter or paste at least two numbers, separated by commas, spaces or new lines. They don't need to be in order.
  2. Choose a quartile method. Median of halves is the one most courses teach. Linear interpolation matches the QUARTILE.INC and PERCENTILE.INC functions in common spreadsheets.
  3. Read the five-number summary as the main result. Each value is listed below it, along with the interquartile range (IQR) and the range.
  4. Check the working to see the sorted data and exactly how Q1 and Q3 were found.

What the inputs mean

Data set
Separate with commas, spaces, or new lines. Don't use thousands separators.
Quartile method
Median of halves: split the sorted data at the median and take the median of each half. With an odd count, the middle value goes in neither half. Linear interpolation: Q1 and Q3 sit at positions 1 + 0.25(n − 1) and 1 + 0.75(n − 1) in the sorted list, where n is how many values you have. When a position falls between two values, it reads off a point part-way between them.

Formula and method

median = middle of the sorted values (mean of the two middle values when n is even)
Median of halves: Q1 = median of the lower half, Q3 = median of the upper half
Linear interpolation: rank r = 1 + p(n − 1), Q = x⌊r⌋ + (r − ⌊r⌋)(x⌊r⌋+1 − x⌊r⌋), with p = 0.25 or 0.75
IQR = Q3 − Q1

In these formulas, n is the number of values. The rank r is a position in the sorted list, and p is the fraction of the way along: 0.25 for Q1 or 0.75 for Q3. The brackets ⌊r⌋ mean r rounded down to a whole number. And x⌊r⌋ is the value at that position in the sorted list.

Both methods agree on the minimum, median and maximum. They only differ in where they put Q1 and Q3. The median-of-halves method always lands on a data value, or halfway between two. The interpolation method treats the sorted values as points along a line. It reads off the spot a quarter and three quarters of the way along.

The two methods give the same quartiles for some data sets and slightly different ones for others. The gap shrinks as the data set grows. Neither is wrong. What matters is using the same method every time.

The IQR (interquartile range) is the width of the middle half of the data. Unlike the range, it ignores the most extreme quarter at each end. So a single unusual value doesn't throw it off.

Worked example

Eleven values: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49, using the median-of-halves method.

  1. The data is already sorted. With 11 values, the median is the 6th value: 40.
  2. Leave out the median. The lower half is 6, 7, 15, 36, 39, so Q1 = 15.
  3. The upper half is 41, 42, 43, 47, 49, so Q3 = 43.
  4. IQR = 43 − 15 = 28.
  5. With linear interpolation instead, Q1 is at position 1 + 0.25 × 10 = 3.5, so Q1 = 15 + 0.5 × (36 − 15) = 25.5. Q3 is at position 8.5, so Q3 = 42 + 0.5 × (43 − 42) = 42.5. That gives IQR = 17.

Result: Five-number summary: 6, 15, 40, 43, 49 (IQR 28) by median of halves. Or 6, 25.5, 40, 42.5, 49 (IQR 17) by linear interpolation.

Understanding the result

If the median sits closer to Q1 than to Q3, the upper part of the data is more spread out. That's a sign of right skew, a longer tail on the high side. The opposite pattern suggests left skew.

A maximum far above Q3, or a minimum far below Q1, hints at outliers, values far from the rest. The usual test flags values more than 1.5 IQRs beyond the quartiles. The outlier calculator applies that test.

The IQR covers the middle 50% of the data. So it's a natural partner to the median when the data is lopsided (skewed).

Assumptions and limitations

  • Every value counts once, and repeated values are kept.
  • With an odd count, the median-of-halves method leaves the median out of both halves. Some textbooks, and Tukey's original "hinges", include it in both halves instead. That can shift Q1 and Q3 slightly for small data sets with an odd count.
  • Other quartile definitions exist, including the spreadsheet QUARTILE.EXC function and several used by statistics software. Their results can differ from both methods here.
  • For very small data sets, quartiles are rough summaries, and the method you choose can change them noticeably.
  • At most 10,000 values.

Frequently asked questions

Why does my textbook or calculator give a different Q1 or Q3?

Quartiles have several accepted definitions. Most intro courses and many handheld calculators use the median of halves. Spreadsheets use linear interpolation. Switch the method to see whether your other answer matches one of them.

Is the median the same as the second quartile?

Yes. Q2 is another name for the median, the point that splits the sorted data into two equal halves. Both methods here work it out the same way.

How is the five-number summary used in a box plot?

The box runs from Q1 to Q3, with a line at the median. The whiskers stretch toward the minimum and maximum. In many box plots, the whiskers stop at the last value inside the outlier limits. Points beyond them are drawn one by one.

What is a good IQR?

There's no one good value. It depends on the units and the situation. Compare it with the median, or with the IQR of a similar data set. That tells you whether the middle of your data is tightly grouped or widely spread.

How this calculator is checked

Method: Median-of-halves quartiles (median excluded for odd n, as taught in introductory statistics) and linear-interpolation quartiles equivalent to spreadsheet QUARTILE.INC (Hyndman & Fan type 7); reference-tested against hand-worked spreadsheet results. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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