We know that the median is the middle number in a set of ordered data. It divides the set of ordered data into two halves.
We also know that for a set of ordered numbers, the median is the number.
If there are numbers,the median is
Similarly, the lower quartile divides the bottom half of the ordered data into two halves
The upper quartile divides the upper half of the ordered data into two halves.
The lower quartile is the value and the upper quartile is the value.
Find the median, lower quartile and upper quartile for the following data:
Ordering the data, we get
There are numbers.
The median is the
The lower quartile ( ) is the
The upper quartile ( ) is the
3,4, ,6,8, ,10,10, ,12,31
Therefore the median is , the lower quartile is and the upper quartile is .
The quartiles are often denoted by and (the median is technically ).
So we could write for the above example: