Finding 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 nnumbers in the list:
The median will be thethnumber . If this is not a data point –iseven – find the averare of thethandthnumber .
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, calculateandround up to the nearest whole number.
whichrounds up to 5. The 5 th number in the list is 4 so thelower quartile is 4.
To find the upper quartile, calculateandround up to the nearest whole number.
whichrounds up to 15. The 15 th number in the list is 8 so theupper quartile is 4.
There is much confusion about how to calculatequartiles because many textbooks have different method. Always checkwith your teacher.