Five Number Summary Calculator - Min, Quartiles & Max

About the Five Number Summary Calculator

The five-number summary describes a whole data set with just five values: the minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. Between them they show where the data is centred, how widely the middle half is spread, and how far the extremes reach. It is the summary that a box-and-whisker plot draws, and it is one of the first things statisticians look at when they meet a new data set.

This five number summary calculator sorts your numbers and finds all five values by either the median-of-halves method taught in most textbooks or the inclusive method used by Excel's QUARTILE.INC. It also gives the range and interquartile range, describes how the box plot would be drawn, comments on the shape of the data, and flags any values beyond the usual 1.5 × IQR outlier fences.

How to Use the Five Number Summary Calculator

Enter your numbers, separated by commas, spaces or new lines. You can paste a column straight from a spreadsheet. At least four values are needed.

Choose the quartile method. Use the median of halves unless your course or software uses the inclusive method.

The five-number summary appears at once, with the supporting figures below it.

The Five Numbers

  minimum   the smallest value
  Q1        the median of the lower half of the data
  median    the middle value (or the mean of the two middle values)
  Q3        the median of the upper half of the data
  maximum   the largest value

With an odd number of values, the textbook method leaves the median itself out of both halves. The inclusive method instead interpolates at positions (n − 1) × 0.25 and (n − 1) × 0.75 in the sorted list, counting the first value as position 0.

Step-by-Step Example

The values 1, 3, 4, 7, 8, 10, 12, 15, 18.

  Sorted:       1, 3, 4, 7, 8, 10, 12, 15, 18   (9 values)
  Minimum:      1
  Median:       the 5th value = 8
  Lower half:   1, 3, 4, 7       → Q1 = (3 + 4) ÷ 2 = 3.5
  Upper half:   10, 12, 15, 18   → Q3 = (12 + 15) ÷ 2 = 13.5
  Maximum:      18

The five-number summary is 1, 3.5, 8, 13.5, 18. The range is 17 and the interquartile range 10. The fences are 3.5 − 15 = −11.5 and 13.5 + 15 = 28.5, so there are no outliers. With the inclusive method, the quartiles become 4 and 12.

A Second Example With an Outlier

The values 2, 3, 5, 7, 9, 120.

  Minimum 2, maximum 120
  Median:       (5 + 7) ÷ 2 = 6
  Lower half:   2, 3, 5    → Q1 = 3
  Upper half:   7, 9, 120  → Q3 = 9
  IQR = 6, upper fence = 9 + 1.5 × 6 = 18

The summary is 2, 3, 6, 9, 120. The box is narrow and balanced, but the upper whisker stretches a long way, and the value 120 lies well beyond the fence of 18.

Drawing a Box Plot

A box plot turns the five-number summary into a picture. Draw a number line, then a box from Q1 to Q3 with a line across it at the median. Lines called whiskers extend from the box toward the minimum and maximum. In the common Tukey style, whiskers stop at the most extreme values still inside the 1.5 × IQR fences, and anything beyond is plotted as a separate dot. Several box plots side by side are one of the clearest ways to compare groups, such as test scores from different classes or delivery times from different depots.

Reading the Shape

The five-number summary reveals the shape of a distribution without a histogram. If the median sits in the middle of the box and the whiskers are similar in length, the data is roughly symmetric. If the upper part of the box and the upper whisker are longer, the data is skewed right, with a tail of high values — typical of incomes, house prices and waiting times. A longer lower side suggests left skew, which is common for exam scores on an easy test, where most students score highly and a few score much lower.

Why Not Just the Mean and Standard Deviation?

The mean and standard deviation are excellent for symmetric data, but both are sensitive to extremes. In the second example the mean is 24.33, larger than five of the six values, and the standard deviation is about 47. The five-number summary describes the same data far more faithfully: most values lie between 3 and 9, around a median of 6, with one extreme value at 120. For skewed data or data with outliers, the median and quartiles are the more honest description.

Understanding Your Result

The headline gives the five numbers in order.

The range and IQR line shows the spread of all the data and of its middle half.

The box plot line describes where the box, median line and whiskers go.

The shape line reads the balance of the box and whiskers.

The outliers line lists any values beyond the 1.5 × IQR fences.

The method line reminds you which quartile method was used.

When Should You Use This Calculator?

Use it to summarise scores, measurements, prices or times in five figures.

Use it to prepare a box-and-whisker plot for a report or homework.

Use it to compare the centre and spread of two or more groups.

Use it as a quick check for skew and outliers before further analysis.

Common Mistakes

Forgetting to sort the data. Every value in the summary depends on the sorted order.

Including the median in both halves. The textbook method leaves it out when the count is odd.

Mixing quartile methods. Spreadsheets and textbooks can give slightly different quartiles for small data sets, so say which one you used.

Drawing whiskers to outliers. In a Tukey box plot the whiskers stop at the fences and outliers are drawn as points.

Reading the box as half the range. The box holds the middle half of the values, not half of the distance between the extremes.

Using too few values. With only four or five numbers, each quartile rests on one or two values and can change a lot if one value changes.