Five Number Summary Calculator
Calculate min, Q1, median, Q3, max for box plot analysis.
Five Number Summary Definition
Minimum: Smallest value in dataset
Q1: First quartile (25th percentile)
Median: Middle value (50th percentile)
Q3: Third quartile (75th percentile)
Maximum: Largest value in dataset
Box Plot Interpretation
| Element | Represents | Interpretation |
|---|---|---|
| Left whisker | Min to Q1 | Bottom 25% of data |
| Left box edge | Q1 | 25th percentile |
| Line in box | Median | 50th percentile (center) |
| Right box edge | Q3 | 75th percentile |
Frequently Asked Questions
What is the five number summary?
Five values that describe data distribution: minimum, Q1, median (Q2), Q3, maximum. Provides complete picture of data spread and center.
What is Q1 (first quartile)?
Q1 marks the 25th percentile. 25% of data below Q1, 75% above. Found by taking median of lower half of data.
What is Q2 (median)?
Q2 is the median, 50th percentile. Half the data below, half above. Also the second quartile.
What is Q3 (third quartile)?
Q3 marks the 75th percentile. 75% of data below Q3, 25% above. Found by taking median of upper half of data.
How do I find Q1 and Q3?
Order data. Find median (splits data in half). Q1 = median of lower half. Q3 = median of upper half.
What is the range?
Range = maximum - minimum. Measures total spread. Single value but doesn't show distribution shape.
What is interquartile range (IQR)?
IQR = Q3 - Q1. Measures middle 50% of data. More informative than range, less affected by outliers.
How is five number summary used in box plots?
Box plot draws box from Q1 to Q3, line at median, whiskers to min/max. Visualizes all five numbers clearly.
What does quartile mean?
Quartile divides data into 4 equal parts (quarters). Q1, Q2, Q3 mark the divisions. Quartiles show data at 25%, 50%, 75% points.
Can I have unequal quartiles?
No. Quartiles always divide data into equal frequency groups (25% each). Position differs with distribution shape, but frequency is equal.
Why use five number summary instead of mean/std dev?
Five number summary is resistant to outliers, shows distribution shape visually, no assumptions about normality. Better for non-normal data.
How does odd vs even count affect quartiles?
Odd count (e.g., 5): median is middle value. Even count (e.g., 6): median is average of two middle. Both methods work consistently.