Question

a statistics student gave a survey to students which asked how many first cousins they have. the data from the first nine responses are shown below. 6, 2, 7, 8, 8, 8, 5, 10, 10 what is the iqr of the data? 2.52 first cousins 3 first cousins 3.5 first cousins 8 first cousins

Explanation:

Step1: Sort the data

$2,5,6,7,8,8,8,10,10$

Step2: Find the median (Q2)

Since there are 9 data - points, the median is the 5th value. So, Q2 = 8.

Step3: Find the lower half

The lower half of the data is $2,5,6,7$. The median of the lower half (Q1) is $\frac{5 + 6}{2}=5.5$.

Step4: Find the upper half

The upper half of the data is $8,8,10,10$. The median of the upper half (Q3) is $\frac{8 + 10}{2}=9$.

Step5: Calculate the IQR

IQR=Q3 - Q1. So, IQR = 9 - 5.5 = 3.5.

Answer:

3.5 first cousins