What Are Quartiles?
Quartiles divide a sorted dataset into four equal parts. The three quartile values -- Q1, Q2, and Q3 -- split the data at the 25th, 50th, and 75th percentiles respectively. Q2 is also known as the median. Quartiles are a fundamental tool in descriptive statistics for understanding the spread and central tendency of data.
The interquartile range (IQR), calculated as Q3 minus Q1, measures the spread of the middle 50% of the data and is widely used to detect outliers. Any data point that falls below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR is typically considered an outlier.
How to Calculate Quartiles
2. Q2 (Median) = middle value of the dataset
3. Q1 = median of the lower half
4. Q3 = median of the upper half
5. IQR = Q3 - Q1
For an odd number of data points, the median is the middle value. For an even number, the median is the average of the two middle values. Q1 is calculated from all values below the median, and Q3 from all values above the median.
Quartile Interpretation
| Quartile | Percentile | Meaning |
|---|---|---|
| Q1 | 25% | 25% of data falls below this value |
| Q2 (Median) | 50% | The middle value of the dataset |
| Q3 | 75% | 75% of data falls below this value |
| IQR | -- | Spread of the middle 50% of data |
Frequently Asked Questions
What is the difference between quartiles and percentiles?
Quartiles are specific percentiles: Q1 is the 25th percentile, Q2 is the 50th percentile, and Q3 is the 75th percentile. Percentiles provide a more granular division -- they split the data into 100 equal parts rather than 4.
How are quartiles used in box plots?
A box plot (box-and-whisker plot) uses Q1, Q2, and Q3 to draw the box, with whiskers extending to the minimum and maximum values (or to 1.5 * IQR from the box edges). Points beyond the whiskers are plotted as individual outliers.