Question

Express the difference in medians as a multiple of the IQR of EACH dataset.Class A.Class B440506070Height (inches)

Answer 1

From the given box plot, let's express the difference in the medians of the IQR of each data.

Given:

Median of class A = 56

Q1 of class A = 50

Q3 of class A = 58

Median of class B = 52

Q1 of class B = 48

Q3 of class B = 54

Thus, we have:

IQR for class A = Q3 - Q1 = 58 - 50 = 8

IQR for class B = Q3 - Q1 = 54 - 48 = 6

Diffrence in median = 56 - 52 = 4

Thus, to find the expression of the difference in medians as a multiple of IQR of each data, we have:

`\begin{gathered} \text{Difference class A: 4 = 8}\ast n \\ \\ \text{Difference class B: 4 = 6 }\ast n \end{gathered}`

Let's solve for each difference.

Difference class A:

`n=(4)/(8)=(1)/(2)`

Difference class B:

`n=(4)/(6)=(2)/(3)`

ANSWER:

`\begin{gathered} \text{CLass A = }(1)/(2) \\ \\ \text{Class B = }(2)/(3) \end{gathered}`