A five-number summary describes a data set with just five values: the minimum, first quartile (Q1), median, third quartile (Q3) and maximum. It shows the center, the spread of the middle half and the full extent of the data at a glance, and it is the recipe for a box-and-whisker plot. This calculator finds all five, lets you pick the quartile method, and draws the box plot for you.
How to use the five number summary calculator
- Paste or type your numbers, separated by commas, spaces or line breaks.
- Choose a quartile method. The default matches TI-84 calculators and most US textbooks.
- Tick Draw outliers separately if you want a modified box plot that marks unusual values with circles.
- Read the summary on the tape and check the sorted halves in Show the work.
How the five numbers are found
With the default method, when the count is odd the median itself belongs to neither half. The quartile calculator explains the four common methods in detail and compares their results.
Worked example
Eleven commute times in minutes: 12, 15, 17, 19, 20, 22, 24, 25, 28, 31, 45.
- The data are already sorted. Minimum = 12 and maximum = 45.
- With 11 values the median is the 6th: 22.
- The lower half is 12, 15, 17, 19, 20, so Q1 = 17.
- The upper half is 24, 25, 28, 31, 45, so Q3 = 28.
The five-number summary is 12, 17, 22, 28, 45. The IQR is 28 − 17 = 11 and the range is 33. The upper fence is 28 + 1.5 × 11 = 44.5, so the 45-minute trip counts as an outlier; with the outlier option on, the right whisker stops at 31 and 45 appears as a separate circle.
Reading a box plot
- The box spans Q1 to Q3 and holds the middle 50% of the data.
- The line inside the box is the median. If it sits off-center, the middle half of the data is skewed.
- The whiskers reach toward the minimum and maximum (or to the fences in a modified plot).
- A long right whisker, or a median pushed toward the left of the box, points to right skew — common for commute times, incomes and wait times.
The calculator also marks the mean with a small ×. In the commute example the mean, about 23.45, sits to the right of the median because the long trip pulls it upward.
Comparing groups
Box plots shine when you put several side by side, for example test scores for three class sections. Compare the medians for center, the box lengths (IQRs) for consistency and the whiskers for extremes. Unlike a mean and standard deviation, the five-number summary is not distorted by a single wild value, which is why introductory statistics courses, including AP Statistics, teach it as the preferred summary for skewed data.
For percentiles other than the quartiles use the percentile calculator, and for averages and spread in one table use the descriptive statistics calculator.
Frequently asked questions
What are the five numbers in a five-number summary?
The minimum, the first quartile (Q1), the median, the third quartile (Q3) and the maximum. Together they split the sorted data into four parts that each hold about a quarter of the values.
Why do different calculators give different quartiles?
There is no single agreed definition. TI calculators and most textbooks take the median of each half and leave the overall median out when n is odd; Excel, Minitab and R interpolate between data points. The method menu lets you match whichever one your class or software uses.
What is a modified box plot?
A box plot whose whiskers stop at the most extreme values inside the fences Q1 − 1.5 × IQR and Q3 + 1.5 × IQR. Values beyond the fences are drawn as separate points so outliers stand out. Tick the outlier option to draw one.
Does a five-number summary need at least five values?
No. The calculator works with any number of values, although with very small data sets some of the five numbers coincide and the summary says little about the shape.