Five-number summary calculator

Paste your numbers to get the minimum, quartiles, median, maximum, IQR and outliers, with a labeled box plot and every step.

  • Free, no sign-up
  • Step-by-step working
  • Runs in your browser

Not sure this is the right tool? Find the right one

  1. 1 Copy and paste your data
  2. 2 Choose an option
  3. 3 Click “Calculate”
  4. 4 Read the result

Tip: No need to type: copy your numbers from Excel, Google Sheets or a CSV file and paste them straight into the box.

This is example data so you can see how the tool works. Replace it with your own: copy your numbers from Excel or Google Sheets and paste them in, or type them.

Paste or type your numbers

Paste a column from Excel or Google Sheets, or separate values with commas, spaces or new lines.

Quartile method (if unsure, keep the default)

Your five-number summary

Open in the box plot maker

How to use the five-number summary calculator

  1. Copy your numbers from Excel or Google Sheets and paste them into the box, or type them separated by commas or spaces. They don't need to be in order.
  2. Keep the TI-84 / textbook quartile method unless your class uses Excel's QUARTILE.INC.
  3. Click Calculate summary.
  4. Read the minimum, Q1, median, Q3 and maximum, the IQR and any outliers, and check the labeled box plot.
  5. Follow the steps to see how each quartile was found, or open the data in the box plot maker for a downloadable chart.

How the five-number summary is calculated

Sort the data from smallest to largest, then:

  • Minimum and maximum: the first and last values.
  • Median: the middle value, or the average of the two middle values when n is even.
  • Q1: the median of the lower half of the data; Q3: the median of the upper half. When n is odd, the overall median is left out of both halves (TI-84 method).

The spread of the middle half, and the fences that decide which values are outliers:

IQR = Q3 − Q1 , fences = Q1 − 1.5 × IQR and Q3 + 1.5 × IQR

Q1
The first quartile: 25% of the data are at or below it
Median
The second quartile: half the data are below it and half above
Q3
The third quartile: 75% of the data are at or below it
IQR
The interquartile range, the width of the middle 50% of the data
Fences
Values beyond 1.5 IQRs below Q1 or above Q3 are flagged as outliers

Worked example

Find the five-number summary of 8 quiz scores: 9, 4, 12, 5, 7, 4, 8, 2.

  1. Sort them
    2, 4, 4, 5, 7, 8, 9, 12
  2. n = 8 is even, so the median is the average of the 4th and 5th values
    Median = (5 + 7) / 2 = 6
  3. Q1 is the median of the lower half (2, 4, 4, 5); Q3 of the upper half (7, 8, 9, 12)
    Q1 = (4 + 4) / 2 = 4, Q3 = (8 + 9) / 2 = 8.5
  4. The five-number summary
    2, 4, 6, 8.5, 12
  5. IQR and outlier fences
    IQR = 8.5 − 4 = 4.5; fences: 4 − 6.75 = −2.75 and 8.5 + 6.75 = 15.25

What it means: half the scores are between 4 and 8.5, the typical score is 6, and since every value is inside the fences there are no outliers. Excel's QUARTILE.INC would give Q3 = 8.25 instead of 8.5, a small difference from the method.

How to interpret the five-number summary

  • Center: the median is the typical value, and isn't pulled by extreme values the way the mean is.
  • Spread: the IQR is the width of the middle half of the data. A bigger IQR means more variation.
  • Shape: if the median is closer to Q1 than to Q3, and the maximum is far out, the data are skewed right. The opposite pattern means skewed left.
  • Outliers: values beyond the fences deserve a second look: a typing error, or a genuinely unusual case.

The box plot maker draws the summary for one or more groups side by side, and the guide to reading a box plot explains each part.

Frequently asked questions

What is the five-number summary?

It is the minimum, first quartile (Q1), median, third quartile (Q3) and maximum of a data set. Together they show the center (the median), the spread of the middle half (Q1 to Q3) and the full range. A box plot is a picture of the five-number summary.

Why do different calculators give different quartiles?

There is no single agreed formula for quartiles. The TI-83/84 and most US textbooks take the median of the lower and upper halves of the data, leaving out the overall median when n is odd: that is the default here. Excel’s QUARTILE.INC (and the older QUARTILE) interpolates between values, and QUARTILE.EXC uses yet another formula. They agree for large data sets but can differ for small ones. Use the method your course or software expects.

How do I find outliers with the IQR?

Use the 1.5 × IQR rule. Calculate IQR = Q3 − Q1, then the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Any value below the lower fence or above the upper fence is an outlier. Some books also call values beyond 3 × IQR “extreme” outliers. The rule flags values to check; it doesn’t mean they are mistakes.

What is the difference between the range and the IQR?

The range is the maximum minus the minimum, so it depends entirely on the two most extreme values and is pulled around by outliers. The IQR is Q3 − Q1, the spread of the middle 50% of the data, so it ignores the extremes. That is why the IQR is the preferred measure of spread for skewed data or data with outliers.

How do I get the five-number summary on a TI-84?

Enter the data in L1 (STAT → 1:Edit), then press STAT, move to CALC and choose 1:1-Var Stats, then ENTER. Scroll down to see minX, Q₁, Med, Q₃ and maxX. The values match this calculator’s default (TI-84) method.

How do I calculate quartiles in Excel or Google Sheets?

Use =MIN(A2:A20), =QUARTILE.INC(A2:A20,1), =MEDIAN(A2:A20), =QUARTILE.INC(A2:A20,3) and =MAX(A2:A20). Google Sheets has QUARTILE and QUARTILE.INC, which work the same way. Pick “Inclusive (Excel QUARTILE.INC)” in this calculator to match them.

Last reviewed November 13, 2026