Quartile Calculator
Calculate Q1, Q2 (median), Q3, interquartile range (IQR), and detect outliers from data.
What Is the Quartile Calculator?
The Quartile Calculator divides a sorted dataset into four equal parts and computes Q1 (25th percentile), Q2 (median), Q3 (75th percentile), and the Interquartile Range (IQR). It also identifies potential outliers using the 1.5×IQR rule and provides a five-number summary.
Formula
How to Use
Enter your data values separated by commas. The calculator sorts them, finds Q1, Q2 (median), and Q3 using the interpolation method, computes the IQR, and flags any values below Q1−1.5×IQR or above Q3+1.5×IQR as potential outliers.
Example Calculation
Data: 4, 7, 10, 14, 19, 23, 32. n=7. Q2=14 (median). Q1=median of lower half {4,7,10}=7. Q3=median of upper half {19,23,32}=23. IQR=23−7=16. Outlier fences: lower=7−24=−17, upper=23+24=47. No outliers.
Understanding Quartile
Quartiles divide an ordered dataset into four equal parts. The first quartile (Q1) marks the 25th percentile — a quarter of the data falls below this value. The median (Q2) marks the 50th percentile, and the third quartile (Q3) marks the 75th percentile. These values summarize the distribution's center and spread in a way that is robust to extreme values.
The interquartile range (IQR = Q3 − Q1) is the most robust measure of statistical spread because it measures the middle 50% of the data, ignoring the extremes. Unlike the range, it is not distorted by outliers. The IQR is central to Tukey's box-and-whisker plot and the 1.5×IQR outlier detection rule.
Quartile analysis is used in income and wealth distribution studies (top and bottom quartiles), educational assessment (quartile rankings), quality control (process capability indices use percentiles), and medical research (reference ranges often expressed as interquartile ranges). Box plots based on the five-number summary provide a visual comparison of distributions across groups.
Frequently Asked Questions
What is the interquartile range (IQR) used for?
The IQR measures statistical spread. It is resistant to outliers, unlike range or standard deviation. The IQR is used in box plots, outlier detection (1.5×IQR rule), and robust statistical analyses.
What are the different methods to calculate quartiles?
There are multiple methods (inclusive, exclusive, Excel, Tukey). This calculator uses the most common method: Q1 is the median of the lower half, Q3 is the median of the upper half (excluding Q2 for odd n).
What is a five-number summary?
The five-number summary consists of: Minimum, Q1, Median (Q2), Q3, Maximum. These five values fully describe a dataset's center and spread and are the basis for box-and-whisker plots.
How do box plots use quartiles?
A box plot draws a box from Q1 to Q3 (the IQR), with a line at the median. Whiskers extend to the most extreme non-outlier values. Points beyond the fences (Q1−1.5IQR, Q3+1.5IQR) are plotted individually as outliers.
Is this calculator free?
Yes, completely free with no account required.