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Sagot :
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:
[tex]\begin{gathered} \text{Difference class A: 4 = 8}\ast n \\ \\ \text{Difference class B: 4 = 6 }\ast n \end{gathered}[/tex]Let's solve for each difference.
Difference class A:
[tex]n=\frac{4}{8}=\frac{1}{2}[/tex]Difference class B:
[tex]n=\frac{4}{6}=\frac{2}{3}[/tex]ANSWER:
[tex]\begin{gathered} \text{CLass A = }\frac{1}{2} \\ \\ \text{Class B = }\frac{2}{3} \end{gathered}[/tex]
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