5 Number Summary Calculator
Enter a list of numbers and get the minimum, first quartile (Q1), median, third quartile (Q3), and maximum, plus the interquartile range, outlier fences, and a box plot.
Enter your data
Paste numbers separated by commas, spaces, or line breaks. Data from a spreadsheet column works directly.
Pick a calculation method
Choose Method 1 (Inclusive, Tukey), Method 2 (Exclusive, TI-83/84), or Method 3 (Percentile, Excel and Google Sheets).
Results
You get the minimum, Q1, median, Q3, maximum, count, range, interquartile range, lower fence, upper fence, and any potential outliers.
Box and whisker plot
The five numbers are drawn as a box plot so you can see the spread and any outliers at a glance.
Worked example
Full step by step calculation using the dataset 4, 8, 15, 16, 23, 42, showing the sort, median, halves, Q1, Q3, IQR, and outlier fences.
Method comparison
Side by side comparison of Tukey, TI-84, and Excel QUARTILE.INC on the same dataset, so you can see where the three methods agree and where they diverge.
Frequently asked questions
What is a five number summary?
A five number summary is five descriptive statistics that describe the shape and spread of a dataset: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum. Together they split the sorted data into four equal-sized groups. A box plot is a picture of those same five numbers.
How do you find Q1 and Q3 by hand?
Sort the values, then find the median. Q1 is the median of the lower half of the data and Q3 is the median of the upper half. Whether you include or exclude the overall median from those halves depends on the method (Tukey includes it when the count is odd, the TI-84 method excludes it). Once you have Q1 and Q3, the interquartile range is Q3 minus Q1.
Why do Excel and my TI-84 give different quartiles?
They use different formulas. The TI-84 excludes the median when it splits the data in half, Tukey's method includes it, and Excel's QUARTILE.INC uses linear interpolation between ranked values. All three are valid, they just answer slightly different questions. Pick the method your class or team uses and stay consistent.
What is the interquartile range used for?
The interquartile range (IQR) measures the spread of the middle 50 percent of your data. It is used to compare variability between groups, to build the box in a box plot, and to flag outliers using the 1.5 times IQR rule. Unlike the standard deviation, the IQR is not pulled around by extreme values.
How do you identify outliers from a five number summary?
Compute the IQR as Q3 minus Q1, then set fences at Q1 minus 1.5 times IQR and Q3 plus 1.5 times IQR. Any value below the lower fence or above the upper fence is a potential outlier. This is Tukey's rule and it is what most statistics classes and box plots use.
What does a box plot show that a histogram does not?
A box plot shows the exact quartiles, the median, and any outliers on one line, which makes it easy to compare several groups side by side. A histogram shows the shape of a single distribution in more detail (peaks, gaps, bins) but hides quartile positions. Use a box plot for comparison and outlier detection, a histogram for shape.