Answer: The interquartile range of this set of data is 19.
Step-by-step explanation:
The values in the given data set : 15, 19, 20, 25, 31, 38, 41
Total values : n= 7
First arrange them in ascending order, we get
15, 19, 20, 25, 31, 38, 41
Lower quartile = [tex]\dfrac{1}{4}(n+1)^{\text{th}}\text{value}[/tex]
[tex]=\dfrac{1}{4}(7+1)^{\text{th}}\text{value}\\\\=2^{\text{nd}}\text{value}\\\\=19[/tex]
Upper quartile = [tex]\dfrac{3}{4}(n+1)^{\text{th}}\text{value}[/tex]
[tex]=\dfrac{3}{4}(7+1)^{\text{th}}\text{value}\\=3(2)^{\text{th}}\text{value}\\=6^{\text{th}}\text{value}\\=38[/tex]
Interquartile range = Upper quartile -Lower quartile
= 38-19=19
Hence, the interquartile range of this set of data is 19.
