10
76
105
147
151
71
141
10
76
105
147
151
71
141
The Five Number Summary Calculator computes the five key values that summarize any numerical dataset: the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum. Together, these five numbers provide a complete snapshot of the data's distribution, center, and spread.
Introduced by the legendary statistician John Tukey in his 1977 book Exploratory Data Analysis, the five-number summary is one of the most powerful and compact tools in descriptive statistics. It forms the basis for the box-and-whisker plot (box plot), which is arguably the most informative single graph for visualizing a dataset's distribution.
Each component of the five-number summary conveys distinct information: the minimum and maximum define the data's overall range; the median identifies the central tendency; and Q1 and Q3 delineate the boundaries of the middle 50% of the data. By examining the spacings between these five values, you can immediately assess skewness, spread, and the presence of potential outliers.
For example, if the distance from the minimum to Q1 is much greater than from Q3 to the maximum, the distribution has a left tail (left-skewed). If Q3 to the maximum greatly exceeds the minimum to Q1, the data is right-skewed. Approximately symmetric data shows roughly equal spacing on both sides of the median.
This calculator accepts up to 10 numeric values, sorts them internally, and computes all five summary values using the inclusive (Tukey) quartile method. It is ideal for students learning descriptive statistics, researchers summarizing experimental data, analysts preparing reports, or anyone who needs a quick, comprehensive overview of a dataset. The five-number summary is universally applicable to any quantitative data: test scores, financial returns, physical measurements, survey responses, and much more.
Unlike measures that assume normality (such as the mean and standard deviation), the five-number summary works well for any distribution shape, including skewed, multimodal, or heavy-tailed distributions. This non-parametric nature makes it a preferred choice in exploratory data analysis.
The five-number summary is computed as follows:
The Range is simply $$\max - \min$$, and the IQR is $$Q3 - Q1$$. These derived measures quantify total spread and central spread, respectively.
Read the five numbers from left to right (min → Q1 → Q2 → Q3 → max) as dividing the data into four groups, each containing approximately 25% of the observations. The gaps between consecutive summary values reveal the distribution's shape: large gaps indicate spread-out data in that region, while small gaps indicate clustering.
If the median is closer to Q1 than to Q3, the data is right-skewed (a longer right tail). If the median is closer to Q3, the data is left-skewed. If the median is roughly centered between Q1 and Q3, and the min-to-Q1 and Q3-to-max distances are similar, the data is approximately symmetric.
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Results
The five-number summary {45, 60, 72.5, 85, 95} shows scores spanning 50 points. The median of 72.5 indicates the typical score. The IQR of 25 points (85-60) covers the middle half of the class.
Inputs
Results
The five-number summary {3200, 4300, 7800, 10300, 12500} reveals right-skew: the gap from Q3 to max (2200) is smaller than min to Q1 (1100), but the gap from median to max (4700) exceeds min to median (4600), suggesting a slight right skew.
A five-number summary consists of the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum of a dataset. These five values divide the data into four quarters, each containing approximately 25% of the observations. It provides a concise yet comprehensive overview of a dataset's center, spread, and shape.
A box plot is the graphical representation of the five-number summary. The box spans from Q1 to Q3 (the IQR), the line inside the box marks the median, and the whiskers typically extend to the minimum and maximum values (or to the fences, with outliers plotted individually). Every box plot is built directly from the five-number summary.
Indirectly, yes. By computing the IQR from Q1 and Q3, you can apply the 1.5 IQR rule: values below Q1 - 1.5*IQR or above Q3 + 1.5*IQR are potential outliers. If the minimum is far below Q1 or the maximum is far above Q3 relative to the IQR, outliers are likely present.
The minimum and maximum are directly affected by outliers. However, Q1, the median, and Q3 are resistant to outliers because they depend only on the relative position of values, not their magnitude. This makes the central three values (Q1, Q2, Q3) robust summary statistics.
Use the five-number summary when your data is skewed, contains outliers, or is non-normal. The mean and standard deviation assume a roughly symmetric distribution and can be misleading for skewed data. The five-number summary makes no distributional assumptions and accurately represents any shape of data.
You need at least 5 data points for a meaningful five-number summary (so each quartile boundary can be distinctly determined). With fewer than 5 values, some of the five numbers will coincide. With 1-3 values, the summary still computes but provides limited insight.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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