What is the 5-Number Summary?

The Five-Number Summary is a set of descriptive statistics that provides a concise snapshot of a dataset's distribution. It was introduced by mathematician John Tukey as part of his Exploratory Data Analysis (EDA) toolkit.

The Five Components

1. Minimum: The smallest value in the dataset. This represents the lower bound of the range (excluding outliers).
2. First Quartile (Q1): The 25th percentile. 25% of the data falls below this value. It marks the beginning of the "middle 50%" of the data.
3. Median (Q2): The 50th percentile. The exact middle value that separates the higher half from the lower half of the data.
4. Third Quartile (Q3): The 75th percentile. 75% of the data falls below this value. It marks the end of the "middle 50%".
5. Maximum: The largest value in the dataset. This represents the upper bound of the range.

Visualizing with Box Plots

The 5-number summary is the raw data used to construct a Box and Whisker Plot:

• The Box is drawn from Q1 to Q3.
• The Line inside the box represents the Median.
• The Whiskers extend from the box to the Minimum and Maximum values.

Why use the 5-Number Summary?

It is superior to using just the Mean (Average) because it gives you information about the skewness and dispersion of the data.

• If the Median is closer to Q1 than Q3, the data is positively skewed (right-skewed).
• If the Median is closer to Q3 than Q1, the data is negatively skewed (left-skewed).
• If the Min and Max are very far from the quartiles, it suggests the presence of outliers.

PlotNerd's 5 Number Summary Calculator instantly generates all five key statistics for quick exploratory data analysis.