Question

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?

Answer 1

Answer with explanation:

From the box and whisker plot of seventh grade we have:

The minimum value =6

First quartile or lower quartile i.e. $Q_1$ = 14

Median or second quartile i.e. $Q_2$ = 18

Third quartile or upper quartile i.e. $Q_3$ =22

and maximum value = 26

From the box and whisker plot of eighth grade we have:

The minimum value =22

First quartile or lower quartile i.e. $Q_1$ = 26

Median or second quartile i.e. $Q_2$ = 30

Third quartile or upper quartile i.e. $Q_3$ = 34

and maximum value = 38

a)

The overlap of the two sets of data is as follows.

• The upper quartile or third quartile of seventh grade is same as the minimum value of the data of eighth grade.
• And the maximum value of seventh grade is same as the lower quartile of eighth grade.

b)

IQR is calculated as the difference of the Upper quartile and the lower quartile

i.e. $Q_3-Q_1$

so, IQR of seventh grade is:

22-14=8

IQR of seventh grade=8

IQR of eighth grade is:

34-26=8

Hence, IQR of eighth grade=8

c)

The difference of the median of the two data sets is:

30-18=12

Hence, the difference of median is: 12

d)

As the IQR of both the sets is same i.e. 8.

Hence, the number that must be multiplied by IQR so that it is equal to the difference between the medians of the two sets is:

$8\times n=12\\\\n=\dfrac{12}{8}\\\\n=\dfrac{3}{2}\\\\n=1.5$

Hence, the number is : 1.5