Sagot :
The interquartile range is a measure of where the “middle fifty” is in a data set, where the bulk of the values lies.
The interquartile range formula is the first quartile subtracted from the third quartile:
[tex]IQR=Q_3-Q_1[/tex]IQR of the Mid-Term
Step 1: Arrange the numbers in order
[tex]73,78,80,81,82,86,87,90,92,95,96[/tex]Step 2: Find the median
[tex]Median\Rightarrow86[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=80[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=92[/tex]Step 4: Calculate the IQR
[tex]IQR=92-80=12[/tex]IQR of the Final
Step 1: Arrange the numbers in order
[tex]75,78,78,78,81,82,83,83,85,85,100[/tex]Step 2: Find the median
[tex]Median\Rightarrow82[/tex]Step 3: Find Q1 and Q3
Q1 and Q3 are the median of the numbers before and after the median of the data set. Therefore, Q1 is the median of the first 5 numbers:
[tex]Q_1=78[/tex]Q3 is the median of the last 5 numbers:
[tex]Q_3=85[/tex]Step 4: Calculate the IQR
[tex]IQR=85-78=7[/tex]ANSWER
The data with the smallest IQR is the FINAL.