The upper quartile, also known as the third quartile or Q3, is a value that marks the 75th percentile of a dataset. It separates the highest 25% of values from the rest. In other words, 75% of the data fall below the upper quartile, and 25% fall above it.
To find the upper quartile:
- Order the data from smallest to largest.
- Divide the dataset into four equal parts.
- The upper quartile is the value that separates the top quarter from the bottom three-quarters.
If the dataset has an even number of values, Q3 is typically calculated as the median of the upper half of the data (not including the overall median if the number of data points is odd).
The upper quartile is commonly used in box plots, where it defines the upper edge of the box, and in identifying outliers when combined with the interquartile range (IQR). Values that fall well above Q3 may be considered unusually high.
For example, if a dataset of test scores has an upper quartile of 88, that means 75% of students scored 88 or lower, and 25% scored higher.
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