Min · Q1 · Median · Q3 · Max — with box plot, IQR, outliers, steps, and easy sharing
The share link reproduces your exact data and settings — paste it in an email, chat, or assignment and anyone who opens it sees the same results.
Saved to this device only (browser local storage). Use a share link to move data between devices.
That is the whole procedure: sort, count, then read off the five values.
Sort the data, then split it at the median into a lower half and an upper half. Q1 is the median of the lower half (the 25th percentile) and Q3 is the median of the upper half (the 75th percentile). Textbooks differ on whether the median itself is included when the count is odd — this calculator supports Tukey (exclude it), Moore & McCabe (include it) and Excel-style interpolation, so you can match whichever method your course uses.
If an observation falls between two points, the general convention is to average the points. There are more complicated approaches (a weighted average) but this usually will suffice.
The second quartile (Q2) is simply the median itself — the 50th percentile. The interquartile range (IQR) is the distance between Q3 and Q1, and it captures the spread of the middle 50% of the data.
You can identify the upper half and lower half of a distribution using the smallest value, middle value, and largest value of the sample. This approach is independent of sample size.
The five number summary maps directly onto a box plot. Draw a box from Q1 to Q3 with a line at the median, so the box spans the middle 50% of the data. Then extend whiskers from the box out to the smallest and largest values that still fall within 1.5 × IQR of the quartiles. Any points beyond the whiskers are plotted individually as outliers.
There is another form of the boxplot referred to as a modified box plot. This adjusts the box and whisker plot so to drop outlier data value points. This calculator now draws the box and whisker plot for you automatically, including outlier points beyond the 1.5 x IQR fences. While the five number summary is a good basic measure of a distribution, it doesn't show a full view of the standard deviation, mean, or variance. You need to carefully manage any suspected outlier data points.
You can use the information from the 5 number summary calculator to calculate this. The upper and lower fences are a simple estimate of the potential outliers of a distribution. This approach uses the interquartile range (Q3 - Q1 values) to assess how far outliers may exist. The inner fence is 1.5 x the interquartile range above / below the 1st and 3rd quartiles (respectively). The outer fence is 3.0 x the interquartile range. Note that the lower bounds of these ranges can be a negative number (this happens when the IQR is wide and Q1 is small or negative). This is common in many logistics problems. In most cases, the underlying data isn't from a normal distribution.
The five number summary is deliberately simple: it describes a dataset using five points — minimum, Q1, median, Q3 and maximum — without assuming the data follows any particular distribution. That makes it a quick, robust first look at almost any sample. The trade-off is that it says nothing about the mean, variance or standard deviation, so it is usually read alongside those measures rather than on its own.
The median marks the centre of the data, while Q1 and Q3 mark the edges of the middle 50%. When the median sits closer to Q1 than to Q3 the distribution is right-skewed, and vice versa. The interquartile range (IQR = Q3 − Q1) measures spread using only the central half of the values, which is why it is far less sensitive to extreme values than the full range or the standard deviation. Any value more than 1.5 × IQR below Q1 or above Q3 is flagged as a potential outlier, and this tool marks those points on the box plot automatically.
Variance is the average squared distance of each value from the mean; the standard deviation is its square root, expressed back in the original units. Both describe how tightly values cluster around the mean. The sample versions (dividing by n − 1) estimate the spread of a wider population from a sample, while the population versions (dividing by n) describe a complete dataset. This calculator reports both, so you can use whichever your assignment or analysis calls for.
Because it makes no distributional assumptions, the five number summary appears wherever people need a fast, honest snapshot of data: comparing test scores across classes, sizing up returns or costs in finance, screening measurements in research, or benchmarking performance in sports and operations. Placing two summaries side by side — which this tool does with its A/B comparison — often reveals differences in centre and spread at a glance, before any heavier statistical test.