Quartile Calculator
Quartile Calculator computes the first (Q1, 25th percentile), second (Q2, median), and third (Q3, 75th percentile) quartiles of a dataset, dividing the data into four equal parts to show distribution.
Enter comma-separated values (e.g., 1,2,3,4):
Methodology Used in Quartile Calculator
The calculator computes quartiles using:
1. Quartile position: \\( P_k = \frac{k}{4} \cdot (n + 1) \\), for \\( k = 1, 2, 3 \\)
2. Quartile value: Linear interpolation between data points at position \\( P_k \\)
Where:
- \\( Q1 \\): First quartile (k=1, 25th percentile)
- \\( Q2 \\): Second quartile (k=2, median)
- \\( Q3 \\): Third quartile (k=3, 75th percentile)
- \\( n \\): Sample size
Sorts data and interpolates for fractional positions.
Example Calculation
Sample Input
Dataset = 1, 2, 3, 4, 5
Step 1: Sort data: \\( 1, 2, 3, 4, 5 \\)
Step 2: Q1 position (k=1): \\( \frac{1}{4} \cdot (5+1) = 1.5 \\), Q1 = \\( 1 + 0.5 \cdot (2 – 1) = 1.5 \\)
Step 3: Q2 position (k=2): \\( \frac{2}{4} \cdot (5+1) = 3 \\), Q2 = \\( 3 \\)
Step 4: Q3 position (k=3): \\( \frac{3}{4} \cdot (5+1) = 4.5 \\), Q3 = \\( 4 + 0.5 \cdot (5 – 4) = 4.5 \\)
Result: Q1 = 1.5, Q2 = 3, Q3 = 4.5.