Statistics • Numerical Descriptive Measures
Enter a set of ungrouped data (individual values). This tool ranks the data, finds the five-number summary (minimum, \(Q_1\), median \(Q_2\), \(Q_3\), maximum), computes the interquartile range \(IQR = Q_3 - Q_1\), and then uses inner fences (\(Q_1 - 1.5\,IQR\), \(Q_3 + 1.5\,IQR\)) and outer fences (\(Q_1 - 3\,IQR\), \(Q_3 + 3\,IQR\)) to classify mild and extreme outliers. Two box-and-whisker diagrams illustrate the construction.
A box-and-whisker plot is based on the five-number summary: minimum, Q1, median (Q2), Q3, and maximum. The box spans Q1 to Q3 and the median is marked inside the box.
The interquartile range measures the spread of the middle 50% of the data. It is computed as IQR = Q3 - Q1.
Inner fences are Q1 - 1.5 x IQR and Q3 + 1.5 x IQR, and outer fences are Q1 - 3 x IQR and Q3 + 3 x IQR. Values beyond the whiskers are outliers, with values between inner and outer fences typically called mild outliers and values outside the outer fences called extreme outliers.
The whiskers extend from the box to the smallest and largest data values that still lie within the inner fences. Any values beyond those whisker endpoints are plotted separately as outliers.
There are multiple accepted quartile rules, especially when the data size is odd or when splitting into halves. Different rules can shift Q1 and Q3 slightly, which changes IQR, fences, and which points are flagged as outliers.