Answer:
IQR= 3
Explanation:
Hello!
The data represents the number of classes taught by each teacher at Broxin High School.
To calculate the IQR you have to do the following steps:
1) Arrange the data from least to greatest:
Raw data: 5, 7, 5, 1, 1, 9, 4, 5, 3, 4, 6
Arranged: 1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
2) Calculate the 1st Quartile (Q₁):
The first quartile divides the bottom 25% of the data from the top 75%, to know which value of the data set corresponds to it you have to calculate its position:
PosQ₁= (n+1)/4= (11+1)/4= 3
This means that the 1st quartile corresponds to the 3rth observation:
1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
Q₁= 3
3) Calculate the 3rd Quartile (Q₃)
The third quartile divides the bottom 75% of the data from the top 25%, as before, you have to calculate its position and then identify the value in the data set.
PosQ₃= (n+1)*(3/4)= (11+1)*(3/4)= 9
The third quartile corresponds to the 9th observation:
1, 1, 3, 4, 4, 5, 5, 5, 6, 7, 9
Q₃= 6
4) Interquartile range (IQR)
The IQR shows you the distance where the middle 50% of the data set is.
IQR= Q₃-Q₁= 6-3 = 3
I hope this helps!