5 Number Summary Calculator

To compute the five-number summary, the calculator first organizes your input numerical values in ascending order from least to greatest. Let the sorted dataset be represented as x = [x1, x2, ..., xn] with n total observations. The minimum is simply x1 and the maximum is xn. The median represents the middle value of the dataset, dividing it into a lower and an upper half. The first quartile (Q1) is the median of the lower half of the data, while the third quartile (Q3) is the median of the upper half. These five values provide a comprehensive non-parametric snapshot of central tendency and dispersion.

Imagine you have a dataset of nine test scores: [55, 70, 75, 80, 85, 90, 92, 95, 100]. First, verify the numbers are in ascending order, which they already are. The minimum value is 55, and the maximum value is 100. The median is the middle number (the 5th value), which is 85. The lower half of the data consists of [55, 70, 75, 80], and the median of this subset is the average of 70 and 75, giving a first quartile (Q1) of 72.5. The upper half consists of [90, 92, 95, 100], and the median of this subset is the average of 92 and 95, yielding a third quartile (Q3) of 93.5. Thus, the five-number summary is: Min = 55, Q1 = 72.5, Median = 85, Q3 = 93.5, Max = 100.

Always ensure your input values are properly separated by commas or spaces and contain only numeric characters to prevent parsing errors. Pay close attention to extreme outliers in your minimum and maximum values, as these can drastically skew your perceived range and interquartile range (IQR). For best results in comparative analysis, keep your dataset sample sizes consistent across different runs.