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 the
th number . If this is not a data point –
is even – find the averare of the
th and
th 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, calculate
and 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, calculate
and 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.
