## Finding the Quartiles and Median of a List of Numbers

To find the median and quartiles of a list of numbers, first sort them – if they are not already sorted. If there are n numbers in the list:

The median will be theth number . If this is not a data point –is even – find the averare of theth andth number .

If the ordered list is

2, 2, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 8, 9, 10, 11

There are 18 numbers in the list.

The 9 ^{th } number is 6 and the 10 ^{th } number is 6. The average of these is 6 so the meduan is 6.

To find the lower quartile, calculateand round up to the nearest whole number.

which rounds up to 5. The 5 ^{th } number in the list is 4 so the lower quartile is 4.

To find the upper quartile, calculateand round up to the nearest whole number.

which rounds up to 15. The 15 ^{th } number in the list is 8 so the upper quartile is 4.

There is much confusion about how to calculate quartiles because many textbooks have different method. Always check with your teacher.