Respuesta :
Answer:
Step-by-step explanation:
IQR is interquartile range of the date. It is the difference between third quartile and first quartile.
[tex]IQR=Q_3-Q_1[/tex]
The marks in first chapter are 75, 85, 88, 92, 92, 95, 95, 100, 100, 100.
Total number of observation is 10.
[tex]Q_1=\frac{n}{4}\text{th term}[/tex]
[tex]Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}[/tex]
It means the first quartile is third term.
[tex]Q_1=88[/tex]
[tex]Q_3=\frac{3n}{4}\text{th term}[/tex]
[tex]Q_3=\frac{30}{4}\text{th term}=7.5\text{th term}[/tex]
It means the third quartile is eighth term.
[tex]Q_3=100[/tex]
[tex]IQR_1=Q_3-Q_1=100-88=12[/tex]
Therefore the IQR of first chapter test is 12.
The marks in final exams are 53, 65, 71, 78, 81, 88, 92, 93, 95, 98.
Total number of observation is 10.
[tex]Q_1=\frac{n}{4}\text{th term}[/tex]
[tex]Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}[/tex]
It means the first quartile is average is third term.
[tex]Q_1=\frac{65+71}{2}=71[/tex]
[tex]Q_3=\frac{3n}{4}\text{th term}[/tex]
[tex]Q_3=\frac{30}{4}\text{th term}=7.5\text{th term}[/tex]
It means the third quartile is eighth term.
[tex]Q_3=93[/tex]
[tex]IQR_1=Q_3-Q_1=93-71=22[/tex]
Therefore the IQR of first chapter test is 22.
So, the IQR of final exam is largest.
