Generate the five-number summary (minimum, Q1, median, Q3, maximum) for any dataset. Calculate IQR, range, mean, standard deviation, detect outliers using Tukey's fences, and visualize data with an interactive box plot.
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Calculate the five-number summary including minimum, first quartile (Q1), median, third quartile (Q3), and maximum. Generate box plots, detect outliers with Tukey's fences, and analyze your data distribution with step-by-step calculations.
The five-number summary is a set of descriptive statistics that provides a concise overview of a dataset's distribution. It consists of: the minimum (smallest value), first quartile Q1 (25th percentile), median Q2 (50th percentile), third quartile Q3 (75th percentile), and maximum (largest value). These five values divide the data into four equal parts and form the basis for box plot visualization, making it easy to identify spread, skewness, and potential outliers.
Five-Number Summary Components
Min, Q₁, Median (Q₂), Q₃, MaxQuickly understand data distribution, identify spread, and detect potential outliers before deeper analysis.
Use side-by-side box plots to compare multiple groups, such as test scores across classes or sales across regions.
Monitor process variation and detect unusual values in manufacturing or service delivery metrics.
Report descriptive statistics for non-normal data in scientific papers and statistical reports.
The exclusive method (TI-83 style) excludes the median when calculating Q1 and Q3, dividing the data into upper and lower halves without including the median in either half. The inclusive method (Tukey's hinges) includes the median in both halves when the dataset has an odd number of values. Both methods are valid; exclusive is common in statistics software and calculators, while inclusive follows Tukey's original definition.
The IQR is calculated as Q3 minus Q1 (IQR = Q3 - Q1). It represents the range of the middle 50% of your data and is a robust measure of spread that is not affected by outliers. The IQR is used to determine Tukey's fences for outlier detection.
Tukey's fences define boundaries for identifying outliers. The lower fence is Q1 - 1.5×IQR and the upper fence is Q3 + 1.5×IQR. Any data point below the lower fence or above the upper fence is considered a potential outlier. This method is robust and does not assume a normal distribution.
In a box plot, the box spans from Q1 to Q3 (the IQR), with a line at the median. Whiskers extend to the minimum and maximum values (or to the fences if showing outliers). The box contains the middle 50% of data. A median closer to Q1 indicates right skew; closer to Q3 indicates left skew. Outliers appear as individual points beyond the whiskers.
Use the five-number summary when your data is skewed, contains outliers, or is not normally distributed. Unlike mean and standard deviation, the five-number summary is based on percentiles and is resistant to extreme values. It's ideal for comparing distributions, describing ordinal data, or when you need a quick visual summary via box plots.