We know that the median divides the data into two halves. We also know that for a set of n ordered numbers, the median is the (n+1)/2 th value.
Similarly, the lower quartile divides the bottom half of the data into two halves and the upper quartile divides the upper half of the data into two halves.
Lower quartile is the (n+1)/4 th value.
Upper quartile is the 3(n+1)/4 th value.
Find the median, lower quartile and upper quartile for the following data:
11, 4, 6, 8, 3, 10, 8, 10, 4, 12, 31
Answer
Ordering the data, we get 3, 4, 4, 6, 8, 8,10, 10, 11, 12, 31
There are 11 numbers.
The median is the (11+1)/2 th = 6th value.
The lower quartile is the (11+1)/4 th = 3rd value.
The upper quartile is the 3(11+1)/4 th = 9th value.
Therefore the median is 8, the lower quartile is 4 and the upper quartile is 11.
3, 4, 4, 6, 8, 8, 10, 10, 11, 12, 31
The interquartile range is the difference between the upper quartile and the
lower quartile. In this example, the interquartile range is 11 - 4 = 7.
Question 2
The interquartile range ignores extreme values. The range includes extreme values.
Look at this set of data:-
1, 5, 7, 8, 9, 12, 13, 15, 17, 18, 35,
The interquartile range is 17 - 7 = 10,
The range is 35 - 1 = 34.
In cases such as these it is often preferable to use the interquartile range when comparing the data.