1.3. Measures of Center http://www.ck12.org
“middle” quartile and is sometimes referred to asQ 2. Some also refer to the minimum value in a data set asQ 0 and
the maximum asQ 4.
Returning to a previous data set:
1 , 1 , 1 , 1 , 1 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 2 , 3 , 3 , 3 , 3 , 3 , 4 , 4 , 5 , 6
Recall that the median (50thpercentile) is 2. The quartiles can be thought of as the medians of the upper and lower
halves of the data.
In this case, there are an odd number of numbers in each half. If there were an even number of numbers, then we
would follow the procedure for medians and average the middle two numbers of each half. Look at the following set
of data:
The median in this set is 90. Because it is the middle number, it is not technically part of either the lower or upper
halves of the data, so we do not include it when calculating the quartiles. However, not all statisticians agree that this
is the proper way to calculate the quartiles in this case. As we mentioned in the last section, some things in statistics
are not quite as universally agreed upon as in other branches of mathematics. The exact method for calculating
quartiles is another one of those topics. To read more about some alternate methods for calculating quartiles in
certain situations, see the following website: