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 between 22 and 26.
The IQR of the seventh grade set is 8 (22-14) and the IQR of the eighth grade set is also 8 (34-26).
The difference between the medians of the two sets is 10 (the median of the seventh grade set is 18 and the median of the eighth grade set is 28).
To find the number that multiplied by the IQR equals the difference between the medians, we can use the formula for the median of a box-and-whisker plot: median = Q1 + (IQR/2).
So, for the seventh grade set, the median is 18 = 14 + (IQR/2), which gives us IQR = 8.
For the eighth grade set, the median is 28 = 26 + (IQR/2), which gives us IQR = 8.
To find the number that multiplied by the IQR equals the difference between the medians, we can set up the equation:
IQR x ? = 10
And solve for the missing number:
8 x ? = 10
? = 10/8 = 1.25
Therefore, 1.25 multiplied by the IQR of either set (8) gives us the difference between the medians (10).