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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 on the number line.
The IQR (interquartile range) 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 4 (30 - 26).
Let x be the number multiplied by the IQR to equal the difference between the medians. Then we have:
x * 8 = 4
Solving for x, we get:
x = 0.5
thanksss
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To find where the two sets of data overlap, we can look at the range of values that are common to both box-and-whisker plots. In this case, we can see that the overlap occurs between the right side of the seventh grade box (22) and the left side of the eighth grade box (26). Therefore, the overlap is in the range from 22 to 26.
To find the IQR (Interquartile Range) for each set, we need to find the difference between the upper quartile (Q3) and the lower quartile (Q1). In the seventh grade plot, Q1 is 14 and Q3 is 22, so the IQR is 22 - 14 = 8. In the eighth grade plot, Q1 is 26 and Q3 is 34, so the IQR is 34 - 26 = 8 as well.
To find the difference between the medians of the two sets, we need to subtract the median of the seventh grade plot from the median of the eighth grade plot. In this case, the median of the seventh grade plot is (14 + 22) / 2 = 18 and the median of the eighth grade plot is (26 + 34) / 2 = 30. Therefore, the difference between the medians is 30 - 18 = 12.
To find the number that, when multiplied by the IQR, equals the difference between the medians of the two sets, we can set up an equation: IQR * x = difference between medians. Using the values we calculated, we get 8 * x = 12. Solving for x, we divide both sides by 8, resulting in x = 1.5.
Therefore, the number that, when multiplied by the IQR, equals the difference between the medians of the two sets, is 1.5.