Quartile numbers divide a dataset into four equal parts. Here's how to find them:
Steps to Calculate Quartiles
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Order the Data: Arrange your dataset in ascending order (from smallest to largest). This is crucial for accurate quartile calculation.
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Find the Median (Q2): The median is the middle value of the dataset. It's also known as the second quartile (Q2).
- If you have an odd number of data points, the median is the central value.
- If you have an even number of data points, the median is the average of the two central values.
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Find the First Quartile (Q1): Q1 is the median of the lower half of the data. This excludes the overall median (Q2) if your original dataset contained an odd number of values.
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Find the Third Quartile (Q3): Q3 is the median of the upper half of the data. Again, this excludes the overall median (Q2) if your original dataset contained an odd number of values.
Example
Let's say you have the following dataset: 6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36
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Order the Data: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
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Find Q2 (Median): There are 11 numbers, so the median is the middle number, which is 40. Q2 = 40
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Find Q1: The lower half of the data is: 6, 7, 15, 36, 39. The median of this lower half is 15. Q1 = 15
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Find Q3: The upper half of the data is: 41, 42, 43, 47, 49. The median of this upper half is 43. Q3 = 43
Quartiles Summary
| Quartile | Description |
|---|---|
| Q1 | 25th percentile, lower quartile |
| Q2 | 50th percentile, median |
| Q3 | 75th percentile, upper quartile |
In summary, finding quartile numbers involves ordering your data, finding the median (Q2), and then finding the medians of the lower and upper halves of the data to determine Q1 and Q3, respectively.
