Question

The table shows the data for a math class's first chapter test marks and the final exam marks. First Chapter Test Final Exam 75 53 85 65 88 71 92 78 92 81 95 88 95 92 100 93 100 95 100 98 Which data set has the largest IQR? First chapter test They have the same IQR There is not enough information to find the IQR Final exam

Answer 1

Answer:

Step-by-step explanation:

IQR is interquartile range of the date. It is the difference between third quartile and first quartile.

$IQR=Q_3-Q_1$

The marks in first chapter are 75, 85, 88, 92, 92, 95, 95, 100, 100, 100.

Total number of observation is 10.

$Q_1=\frac{n}{4}\text{th term}$

$Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}$

It means the first quartile is third term.

$Q_1=88$

$Q_3=\frac{3n}{4}\text{th term}$

$Q_3=\frac{30}{4}\text{th term}=7.5\text{th term}$

It means the third quartile is eighth term.

$Q_3=100$

$IQR_1=Q_3-Q_1=100-88=12$

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.

$Q_1=\frac{n}{4}\text{th term}$

$Q_1=\frac{10}{4}\text{th term}=2.5\text{th term}$

It means the first quartile is average is third term.

$Q_1=\frac{65+71}{2}=71$

$Q_3=\frac{3n}{4}\text{th term}$

$Q_3=\frac{30}{4}\text{th term}=7.5\text{th term}$

It means the third quartile is eighth term.

$Q_3=93$

$IQR_1=Q_3-Q_1=93-71=22$

Therefore the IQR of first chapter test is 22.

So, the IQR of final exam is largest.