The lower quartile, also known as the first quartile or Q1, marks the 25th percentile of a dataset. It separates the lowest 25% of values from the highest 75%. In other words, one-quarter of the data fall at or below the lower quartile, while the remaining 75% lie above it.
To find the lower quartile:
- Sort the data in ascending order.
- Divide the dataset into four equal parts.
- The lower quartile is the value that marks the boundary between the first and second quarters of the data.
If the dataset has an even number of values, Q1 is typically the median of the lower half of the data. If the number of values is odd, most methods exclude the overall median when identifying the lower half.
The lower quartile is a key component of box plots, where it defines the bottom edge of the box and helps calculate the interquartile range (IQR). Analysts use the IQR and Q1 to detect potential outliers, which often fall far below the lower quartile.
For example, in a dataset of commute times, if the lower quartile is 18 minutes, it means that 25% of people have commutes of 18 minutes or less, and 75% commute longer.
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