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.
How do I figure out how to do b,c,d?
The box and whisker plot shows the number of text messages received in one day by students in seventh and eighth grade at Lincoln Middle School.
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?
To answer parts b, c, and d of the question, we need to understand some basic concepts related to box and whisker plots.
A box and whisker plot is a visual representation of a set of data which shows the minimum, first quartile (Q1), median, third quartile (Q3), and maximum values. The range of the data is represented by the distance between the minimum and maximum values, while the interquartile range (IQR) represents the range between the first quartile and third quartile.
Now, let's address each part of the question:
a) Describe the overlap of the two sets of data:
To determine the overlap of the two sets of data, we observe the range of values represented by each box on the plots. In this case, the seventh-grade plot ranges from 6 to 26, while the eighth-grade plot ranges from 22 to 38. Therefore, there is an overlap between the two sets of data from the value of 22 to 26.
b) Find the IQR of each set:
The IQR is the range between the first quartile (Q1) and the third quartile (Q3). From the information provided, the seventh-grade plot has a Q1 at 14 and a Q3 at 22, resulting in an IQR of 22 - 14 = 8. The eighth-grade plot has a Q1 at 26 and a Q3 at 34, resulting in an IQR of 34 - 26 = 8.
c) Find the difference between the medians of the sets:
The median is the middle value of a set of data. From the information provided, the seventh-grade plot has a median at 18, while the eighth-grade plot has a median at 30. Therefore, the difference between the two medians is 30 - 18 = 12.
d) What number multiplied by the IQR equals the difference between the medians of the two sets?
To find the number that, when multiplied by the IQR, gives the difference between the medians, we divide the difference between the medians by the IQR:
12 / 8 = 1.5
Therefore, the number that, when multiplied by the IQR, equals the difference between the medians of the two sets is 1.5.