Quartile Calculator
Calculate Q1, Q2 (median), Q3, and interquartile range (IQR)
Data Input
Step-by-Step Example
Example: Test Scores
Raw data: 32, 21, 38, 12, 44, 42, 37, 36
Sorted: 12, 21, 32, 36, 37, 38, 42, 44
Count (n): 8 values
Calculation Steps
Q1: Median of first half [12, 21, 32, 36] = (21 + 32) / 2 = 26.5
Q2 (Median): Middle of all values = (36 + 37) / 2 = 36.5
Q3: Median of second half [37, 38, 42, 44] = (38 + 42) / 2 = 40
IQR: Q3 - Q1 = 40 - 26.5 = 13.5
Understanding Quartiles
Q1 (25th Percentile)
25% of values are below this point
Q2 (50th Percentile)
The median - 50% of values are below
Q3 (75th Percentile)
75% of values are below this point
IQR (Interquartile Range)
Middle 50% spread (Q3 - Q1)
Key Applications
Data Analysis: Understand data distribution and spread
Outlier Detection: Values beyond 1.5×IQR from quartiles
Box Plots: Five-number summary visualization
Percentile Analysis: Compare individual values to dataset
Understanding Quartiles in Statistics
What are Quartiles?
Quartiles divide a dataset into four equal parts, each containing 25% of the data points. They provide a robust way to understand the distribution and spread of your data, especially when dealing with skewed distributions or outliers.
The Five-Number Summary
- •Minimum: The smallest value in the dataset
- •Q1: The first quartile (25th percentile)
- •Q2: The second quartile (median, 50th percentile)
- •Q3: The third quartile (75th percentile)
- •Maximum: The largest value in the dataset
Calculation Methods
For even n:
Q1 = median of lower half
Q2 = (middle values)/2
Q3 = median of upper half
For odd n:
Q1 = median of lower half (including middle)
Q2 = middle value
Q3 = median of upper half (including middle)
Interquartile Range (IQR)
The IQR measures the spread of the middle 50% of the data. It's calculated as Q3 - Q1 and is particularly useful for identifying outliers and understanding data variability without being affected by extreme values.
Practical Applications
Education
Analyze test scores to understand student performance distribution and identify students who need additional support.
Business Analytics
Evaluate sales performance, customer satisfaction scores, and market research data to make informed decisions.
Quality Control
Monitor manufacturing processes and product quality by analyzing measurement distributions and identifying outliers.