Question

The box plot shows the algebra scores of students in class A and class B.



The median score of class A is _____.

The interquartile range of class B is ____.

The difference of the medians of class A and class B is
the interquartile range of either data set.

Answer 1

Answer:

$Mid(A) = 73$

$IQR(B) = 8$

The difference of the medians of class A and class B is between  the interquartile range of either data set.

Step-by-step explanation:

Given

The attached box plots

To answer this, see attached image for how to read a box plot

With reference to the attached image of how to read the box plot;

Solving (a): The median of class A

$Mid(A) = 73$

Solving (b): IQR of class B

IQR is calculated as:

$IQR =Q_3 - Q_1$

From the box plot of class B, we have:

$Q_3 = 87$

$Q_1 = 79$

So, we have:

$IQR(B) = 87 - 79$

$IQR(B) = 8$

Solving (c):

$Mid(A) = 73$

$Mid(B) = 82$

$IQR(B) = 8$

IQR of class A is calculated as:

$IQR =Q_3 - Q_1$

From the box plot of class A, we have:

$Q_3 = 76$

$Q_1 = 68$

So, we have:

$IQR(A) = 78 - 68$

$IQR(A) = 10$

The difference (d) between the medians is:

$d =Mid(B) - Mid(A)$

$d = 82 - 73$

$d = 9$

From $smallest$ to $largest$, we have: 8, 9, 10

i.e. IQR(B), d, IQR(A)