Third Quartile Calculator
Calculate Q3, quartiles, and statistical measures from your dataset
Enter Your Dataset
⚠️ Enter at least 2 values to calculate quartiles
Quartile Quick Reference
Q1 (First Quartile)
25th percentile
25% of data below this value
Q2 (Median)
50th percentile
Middle value of dataset
Q3 (Third Quartile)
75th percentile
75% of data below this value
IQR
Interquartile Range
Q3 - Q1 (middle 50% spread)
Example: Test Scores
Q1: 75 (25% scored below 75)
Q2: 83.5 (median score)
Q3: 90 (75% scored below 90)
IQR: 15 (middle 50% range)
How to Calculate Q3
Sort data in ascending order
Find upper half of dataset
Calculate median of upper half
That's your third quartile!
Understanding the Third Quartile
What is the Third Quartile?
The third quartile (Q3), also called the upper quartile, is the value that separates the highest 25% of data from the lowest 75%. It represents the 75th percentile of your dataset, meaning three-quarters of all data points fall below this value.
Why is Q3 Important?
- •Identifies the upper boundary of the middle 50% of data
- •Essential for creating box plots and detecting outliers
- •Helps understand data distribution and skewness
- •Used in calculating the Interquartile Range (IQR)
Calculation Method
Step 1: Sort data in ascending order
Step 2: Determine upper half of data
• Even n: Take upper half after splitting
• Odd n: Exclude median, take upper values
Step 3: Find median of upper half
• Odd length: Middle value
• Even length: Average of two middle values
Related Measures
IQR = Q3 - Q1: Range containing middle 50% of data
Semi-IQR = IQR ÷ 2: Half of interquartile range
Outlier Boundary: Q3 + 1.5 × IQR (upper fence)
Box Plot Connection: In a box plot, Q3 forms the right edge (or top edge) of the central box, with the box width representing the IQR.
Applications and Examples
📊 Academic Performance
Use: Analyze test score distributions
Example: If Q3 = 85 on a 100-point test
Meaning: 75% of students scored 85 or below
Insight: Top 25% scored above 85
💰 Income Analysis
Use: Understand income distribution
Example: If Q3 = $75,000 annual salary
Meaning: 75% earn $75K or less
Insight: Identifies high earners (top 25%)
⏱️ Performance Metrics
Use: Analyze response times or speeds
Example: Q3 = 2.5 seconds load time
Meaning: 75% of pages load in ≤2.5s
Insight: 25% need optimization