Question

The following data points represent the number of classes that each teacher at Broxin High School teaches.

Answer 1

Answer:

IQR= 3

Step-by-step 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!