What is the formula for calculating the upper quartile?

The upper quartile is calculated by finding the median of the upper half of a data set.

To calculate the upper quartile (also known as the third quartile, Q3), you first need to arrange your data set in ascending order. Once the data is ordered, you can find the median, which is the middle value of the data set. If the number of data points (n) is odd, the median is the middle number. If n is even, the median is the average of the two middle numbers.

After finding the median, you split the data set into two halves. The upper quartile is the median of the upper half of the data set. If the number of data points in the upper half is odd, the upper quartile is the middle number of this half. If it is even, the upper quartile is the average of the two middle numbers in the upper half.

For example, consider the data set: 3, 7, 8, 12, 13, 14, 18, 21, 23, 27. First, find the median, which is the average of the 5th and 6th values: (13 + 14) / 2 = 13.5. The lower half is 3, 7, 8, 12, 13, and the upper half is 14, 18, 21, 23, 27. The median of the upper half (14, 18, 21, 23, 27) is 21, so the upper quartile (Q3) is 21.

This method ensures you accurately find the upper quartile, which helps in understanding the spread and distribution of your data.