5 Number Summary Calculator

A five-number summary condenses a numerical data set into its minimum, first quartile, median, third quartile, and maximum. Together these landmarks describe location, spread, and potential asymmetry without assuming a particular probability distribution. They are the values used to draw a box-and-whisker plot: the box spans Q1 to Q3, a line marks the median, and whiskers extend toward the lowest and highest observations under the plotting convention being used. The calculator first sorts every observation from smallest to largest. The minimum and maximum are the endpoints, and the median is the middle value or the average of the two middle values. It then uses the median-of-halves method for quartiles. When the sample size is odd, the overall median is excluded before finding the medians of the lower and upper halves. When it is even, the sorted values divide into equal halves. Q1 is the median of the lower half and Q3 is the median of the upper half. Quartiles divide ordered data into four broad sections. Roughly 25 percent of observations lie at or below Q1, half lie at or below the median, and 75 percent lie at or below Q3. The interquartile range, IQR = Q3 − Q1, measures the width of the middle half of the data. Unlike the full range, it is relatively resistant to extreme observations, which makes it helpful for comparing distributions and identifying possible outliers. Several accepted quartile conventions exist, especially for small data sets, so software packages may produce slightly different Q1 and Q3 values. This calculator states and consistently applies the median-of-halves convention. Use the method required by your course, organization, or statistical package when exact agreement matters. Repeated values and negative values are valid, and the input order does not affect the result because all observations are sorted first. A five-number summary is most informative alongside the sample size and subject context. Two data sets can share all five values while differing between those landmarks. It also does not report the mean or standard deviation. Use it for quick exploratory analysis, box plots, skewness clues, and robust comparisons, then inspect the underlying observations or additional statistics before drawing substantive conclusions.