1. What are Quartiles and IQR?

Quartiles divide a ranked dataset into four equal parts. Q1 (first quartile) is the median of the lower half, Q3 (third quartile) is the median of the upper half. The IQR (interquartile range) measures statistical dispersion between Q1 and Q3.

2. How Does the Calculator Work?

The calculator uses the following method:

Where:

• \( Q1 \) — First quartile (25th percentile)
• \( Q3 \) — Third quartile (75th percentile)
• \( IQR \) — Interquartile range (Q3 - Q1)

Explanation: The calculator sorts the data and finds the values at the 25th and 75th percentiles, then calculates the difference between them.

3. Importance of Quartiles and IQR

Details: Quartiles and IQR are essential for understanding data distribution, identifying outliers, and comparing datasets. Unlike range, IQR is not affected by extreme values.

4. Using the Calculator

Tips: Enter numeric values separated by commas. The calculator will sort the data and compute Q1, Q3, and IQR. At least 4 data points are recommended for meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between quartiles and percentiles?
A: Q1 is the 25th percentile, Q2 (median) is the 50th percentile, and Q3 is the 75th percentile.

Q2: How is IQR used to identify outliers?
A: Typically, values below Q1-1.5×IQR or above Q3+1.5×IQR are considered outliers.

Q3: What's better - range or IQR?
A: IQR is generally better as it's less affected by extreme values, giving a more robust measure of spread.

Q4: Can I calculate quartiles for small datasets?
A: Yes, but interpretation requires caution with fewer than 10 data points.

Q5: How are quartiles represented visually?
A: Typically shown in box plots, where the box represents Q1 to Q3 with a line at the median.