Question

Here are Barry Bonds's home-run totals, mostly for the San Francisco Giants, during the years 1991 - 2005:25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5There are two outliers at opposite ends of this distribution: his 5 home runs in 2005 and his 73 home runs in 2001. Which of the following is a modified box plot for this distribution?

Answer 1

Answer:

Refer the attached figure.

Step-by-step explanation:

Given : Here are Barry Bonds's home-run totals, mostly for the San Francisco Giants, during the years 1991 - 2005

The data A={25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45}  

To find : Modified box plot for this distribution?

Solution :

Arranging the data from lowest to highest,

{25,33,34,34,37,37,40,42,45,45,46,46,49,73}  

Find the median of the data  

As the data is even numbers so the median is

$M=\frac{40+42}{2}=\frac{82}{2}=41$

Median = 41

For Box plot Graph,

$q_1=Q(A,0)$

$q_1=25$

$q_2=Q(A,0.25)$

$q_2=34.75$

$q_3=Q(A,0.5)$

$q_3=41$

$q_4=Q(A,0.75)$

$q_4=45.75$

$q_5=Q(A,1)$

$q_5=73$

Plotting the Box plot of the data.

Refer the attached figure below.

Answer 2

Answer:

The box plot of given data is shown below.

Step-by-step explanation:

The given data set is

25, 34, 46, 37, 33, 42, 40, 37, 34, 49, 73, 46, 45, 45, 5

Arrange the data in ascending order.

5, 25, 33, 34, 34, 37, 37, 40, 42, 45, 45, 46, 46, 49, 73

Divide the data in 4 equal parts.

(5, 25, 33), 34,( 34, 37, 37), 40,( 42, 45, 45), 46, (46, 49, 73)

Minimum = 5

Maximum = 73

$Q_1=34$

$Median=40$

$Q_3=46$

The interquartile range of the data set is

$IQR=Q_3-Q_1$

$IQR=46-34=12$

Boundaries are:

$Minimum=Q_1-1.5(IQR)\Rightarrow 34-1.5(12)=16$

$Maximum=Q_3-1.5(IQR)\Rightarrow 46+1.5(12)=64$

In range of the box plot is 16 to 64. Box starts from 34 and ends at 46 and mark a line inside the box at 40. Plot one dot above 5 and one dot above 73.

Therefore, the box plot of given data is shown below.