Question

1. the following data set represents the number of students who attended monday swim classes. 8, 6, 4, 3, 8, 9, 6, 5, 2, 8 q1: ______ q3: ____ iqr: ______

Explanation:

Step1: Sort the data set

$2,3,4,5,6,6,8,8,8,9$

Step2: Find the median (Q2)

There are $n = 10$ data - points. The median is the average of the 5th and 6th ordered values. So, $Q2=\frac{6 + 6}{2}=6$.

Step3: Find Q1

The lower half of the data set is $2,3,4,5,6$. Since there are $n = 5$ data - points in the lower half, the median of the lower half (Q1) is the 3rd value. So, $Q1 = 4$.

Step4: Find Q3

The upper half of the data set is $6,8,8,8,9$. Since there are $n = 5$ data - points in the upper half, the median of the upper half (Q3) is the 3rd value. So, $Q3 = 8$.

Step5: Calculate the IQR

$IQR=Q3 - Q1$. Substituting the values of Q1 and Q3, we get $IQR=8 - 4=4$.

Answer:

Q1: 4
Q3: 8
IQR: 4