Short Answer
Note: Your teacher will grade your response to ensure you receive proper credit for your answer.
The box-and-whisker plot below shows the numbers of text messages received in one day by students in the seventh and eighth grades at Lincoln Middle School.
Two box and whisker plots are shown above a number line.
The number line is scaled from 2 to 38 by twos.
The first plot above the number line is labeled seventh grade.
On the seventh grade plot:
The left point is at 6. The left side of the box is at 14. The vertical segment inside the box is at 18 . The right side of the box is at 22. The right point of the plot is at 26.
The eighth grade plot is above the seventh grade plot.
On the eighth grade plot:
The left point is at 22. The left side of the box is at 26. the vertical segment inside the box is at 30. The right side of the box is at 34. The right point of the plot is at 38.
Where do the two sets of data overlap?
Find the IQR of each set.
Find the difference between the medians of the sets.
What number multiplied by the IQR equals the difference between the medians of the two sets?
The two sets of data overlap from 22 to 26 (inclusive).
IQR of the seventh grade set: 22 - 14 = 8
IQR of the eighth grade set: 34 - 26 = 8
Difference between medians: 30 - 18 = 12
Let x be the number multiplied by the IQR. Then,
x(8) = 12
x = 1.5
Therefore, 1.5 multiplied by the IQR equals the difference between the medians of the two sets.