1. What is the First Quartile (Q1)?

The first quartile (Q1) is the median of the lower half of a dataset. It marks the value below which 25% of the data falls. Quartiles divide ordered data into four equal parts, with Q1 representing the 25th percentile.

2. How to Calculate Q1

The steps to calculate Q1:

Example: For dataset [3,5,7,8,12,13,14,18,21]

• Sorted data: [3,5,7,8,12,13,14,18,21]
• Lower half (values below median 12): [3,5,7,8]
• Q1 = median of lower half = (5+7)/2 = 6

3. Importance of Quartiles

Details: Quartiles are essential in descriptive statistics for understanding data distribution. They are used in box plots, identifying outliers, and comparing datasets. The interquartile range (IQR = Q3-Q1) measures statistical dispersion.

4. Using the Calculator

Tips: Enter your numerical data points separated by commas. The calculator will sort the data and compute Q1, median (Q2), and Q3. Empty or non-numeric values will be ignored.

5. Frequently Asked Questions (FAQ)

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

Q2: How do you calculate Q1 for an even number of data points?
A: Include the median in neither half (common method) or include it in both halves (Tukey's method). Our calculator uses the first approach.

Q3: What if my dataset has an odd number of values?
A: The median (Q2) is excluded from both halves when calculating Q1 and Q3.

Q4: Can quartiles be calculated for categorical data?
A: No, quartiles require numerical data that can be ordered.

Q5: How are quartiles used in box plots?
A: Box plots show Q1, Q2, Q3 as the box edges and line, with "whiskers" extending to non-outlier min/max values.