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. a) Describe the overlap of the two sets of data. b) Find the IQR of each set. c) Find the difference between the medians of the sets. d) What number multiplied by the IQR equals the difference between the medians of the two sets?

Here's some help. Let me know if you need any more help!

a) The ranges of the two sets of data overlap by 4.
The upper quartile of the 7th grade data equals the lowest value of the 8th grade data.
The highest value of the 7th grade data equals the lower quartile of the 8th grade data.

b) IQR of the 7th grade data = 22 - 14 = 8
IQR of the 8th grade data = 34 - 26 = 8

c) median difference = 30 - 18 = ____

d) 8*x = answer to c)
x = ____

uh uh Sbeve.

props to anyone who gets that reference. :3

thanks

a) To describe the overlap of the two sets of data, we need to compare the ranges of the data sets. The range of the seventh grade data set is from 6 to 26, while the range of the eighth grade data set is from 22 to 38. Therefore, the overlap between the two sets is from 22 to 26, as those are the common values in both sets.

b) To find the IQR (interquartile range) of each set, we need to calculate the difference between the first quartile (Q1) and the third quartile (Q3) for each set.

For the seventh grade data set:
Q1 = 14
Q3 = 22
IQR = Q3 - Q1 = 22 - 14 = 8

For the eighth grade data set:
Q1 = 26
Q3 = 34
IQR = Q3 - Q1 = 34 - 26 = 8

So, the IQR for both sets is 8.

c) To find the difference between the medians of the two sets, we need to subtract the median of the seventh grade data set from the median of the eighth grade data set.

The median of the seventh grade data set is (18 + 22) / 2 = 20.
The median of the eighth grade data set is (30 + 34) / 2 = 32.

Difference = Median of eighth grade - Median of seventh grade = 32 - 20 = 12.

d) To find the number that, when multiplied by the IQR, equals the difference between the medians of the two sets, we can set up the equation:

x * IQR = Difference

Substituting the values we found:
x * 8 = 12

To solve for x, divide both sides of the equation by 8:
x = 12 / 8 = 1.5

So, the number that, when multiplied by the IQR, equals the difference between the medians of the two sets, is 1.5.