First arrange the values in ascending order:-
4, 5, 6, 6, 7, 8, 9, 9, 10, 10, 12, 12, 14, 15,
The first quartile is 6 and the third is 12
So the difference is 12- 6 = 6 (answer)
The difference or the gap between the two quartiles that is quartile 3 and quartile 1 is 6.
The difference is determined in a specific order:
1. First the given numbers are arranged into ascending order:
4,5,6,6,7,8,9,9, 10,10,12,12,14,15
2. Now find quartile 2 that is the median from taking the middle number.
In the given case there are even numbers, so the 2 middle numbers are taken are 9 and 9; and the sum of the middle numbers will be divided by 2 for determining quartile 2.
[tex]\rm{Quartile}\;2=\dfrac{9+9}{2}\\=\dfrac{18}{2}\\=9[/tex]
3. Now find quartiles 1 and 3:
The middle number for quartile 1 is 6, it is taken from the above numbers in ascending order; that is from 4,5,6,6,7,8,9.
Same way, the middle number for quartile 3 is 12, it is taken from the above numbers in ascending order, that is from 9,10,10,12,12,14,15.
4. Finally the difference between Q1 and Q3 is 6 that is the difference between 12 and 6.
To know more about quartiles, refer to the link:
https://brainly.com/question/7039036
