First Quartile Calculator
Calculate Q1 (25th percentile), median, quartiles, and statistical measures for your data set
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Quartile Definitions
First Quartile (Q1)
The 25th percentile - divides the lowest 25% of data from the rest
Second Quartile (Q2)
The median - divides data into two equal halves (50th percentile)
Third Quartile (Q3)
The 75th percentile - divides the lowest 75% of data from the top 25%
Interquartile Range (IQR)
Q3 - Q1, measures the spread of the middle 50% of data
How to Calculate Q1
Sort Data
Arrange all values in ascending order
Find Lower Half
Split data at median, take lower portion
Calculate Median
Find median of the lower half = Q1
Box Plot Elements
Left Edge (Q1)
First quartile marks the left boundary of the box
Center Line (Q2)
Median line inside the box
Right Edge (Q3)
Third quartile marks the right boundary
Whiskers
Extend to minimum and maximum values
Understanding First Quartile (Q1)
What is the First Quartile?
The first quartile (Q1) is a positional measure that divides a sorted dataset so that 25% of the data points fall below it and 75% fall above it. It's also known as the 25th percentile or lower quartile.
Key Properties
- •Represents the 25th percentile of the data
- •Used in five-number summary statistics
- •Essential for creating box plots
- •Helps identify data distribution patterns
Calculation Methods
Median-Based Method
- 1. Sort data in ascending order
- 2. Find the median position
- 3. Split data at median (exclude median for odd n)
- 4. Calculate median of lower half = Q1
Applications
- ✓Quality control and process monitoring
- ✓Educational assessment and grading
- ✓Financial analysis and risk assessment
- ✓Medical research and health statistics
Quartiles in Normal Distribution
For any normal distribution with mean μ and standard deviation σ:
Q1 = μ - 0.67448σ
First quartile is approximately 0.674 standard deviations below the mean
Q2 = μ
Median equals the mean in normal distributions
Q3 = μ + 0.67448σ
Third quartile is approximately 0.674 standard deviations above the mean