Question

The data set shown below contains the number of hurricanes that occurred each year over a​ 14-year period. Some scientists claim that there has been

an increasean increase

in the number of hurricanes as the years progressed. Complete parts​ a) through​ d).

Year	11	22	33	44	55	66	77	88	99	1010	1111	1212	1313	1414
​#	11	22	22	00	22	33	33	11	11	22	44	11	11	00

​a) Create a histogram of these data.

Choose the correct histogram below.

A.

0506# of Hurricanes

A histogram has a horizontal axis labeled "Number of Hurricanes" from 0 to 5 in increments of 1 and a vertical axis labeled from 0 to 6 in increments of 1. The histogram has vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the height is listed second: 0, 2; 1, 5; 2, 4; 3, 2; 4, 1.

B.

0506# of Hurricanes

A histogram has a horizontal axis labeled "Number of Hurricanes" from 0 to 5 in increments of 1 and a vertical axis labeled from 0 to 6 in increments of 1. The histogram has vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the height is listed second: 0, 1; 1, 2; 2, 4; 3, 3; 4, 4.

C.

0506# of Hurricanes

A histogram has a horizontal axis labeled "Number of Hurricanes" from 0 to 5 in increments of 1 and a vertical axis labeled from 0 to 6 in increments of 1. The histogram has vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the height is listed second: 0, 2; 1, 2; 2, 3; 3, 5; 4, 2.

D.

0506# of Hurricanes

A histogram has a horizontal axis labeled "Number of Hurricanes" from 0 to 5 in increments of 1 and a vertical axis labeled from 0 to 6 in increments of 1. The histogram has vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the height is listed second: 0, 2; 1, 3; 2, 4; 3, 3; 4, 2.

​b) Describe the distribution.

Is the distribution​ uniform, unimodal, or​ bimodal?

A.The distribution is

uniformuniform.

B.The distribution is

unimodalunimodal.

C.

The distribution is bimodal.

Is the distribution symmetric or​ skewed?

A.The distribution is

skewed to the rightskewed to the right.

B.The distribution is

skewed to the leftskewed to the left.

C.The distribution is

symmetricsymmetric.

Which of the following statements best describes the center of the​ distribution?

A.The center is best described by the​ mean,

1.641.64

hurricanes.

B.The center is best described by the​ median,

1.51.5

hurricanes.

C.The center is best described by the

medianmedian​,

22

hurricanes.The range of the data is

nothing

hurricanes.

Describe any unusual features.

A.

There is one year with an unusually low number of hurricanes.

B.

There are no unusual features.

C.As the years​ progressed, the number of hurricanes

increasedincreased.

D.

There is one year with an unusually large number of hurricanes.

​c) Create a time series plot of these data.

Choose the correct graph below.

A.

01606Year# of Hurricanes

A coordinate system has a horizontal axis labeled Year from 0 to 16 in increments of 2 and a vertical axis labeled Numer of Hurricanes from 0 to 6 in increments of 1. Fourteen plotted points are connected by line segments from left to right and have coordinates as follows: (1, 0), (2, 0), (3, 1), (4, 1), (5, 1), (6, 1), (7, 1), (8, 2), (9, 2), (10, 2), (11, 2), (12, 3), (13, 3), (14, 4).

B.

01606Year# of Hurricanes

A coordinate system has a horizontal axis labeled Year from 0 to 16 in increments of 2 and a vertical axis labeled Numer of Hurricanes from 0 to 6 in increments of 1. Fourteen plotted points are connected by line segments from left to right and have coordinates as follows: (1, 0), (2, 1), (3, 1), (4, 4), (5, 2), (6, 1), (7, 1), (8, 3), (9, 3), (10, 2), (11, 0), (12, 2), (13, 2), (14, 1).

C.

01606Year# of Hurricanes

A coordinate system has a horizontal axis labeled Year from 0 to 16 in increments of 2 and a vertical axis labeled Numer of Hurricanes from 0 to 6 in increments of 1. Fourteen plotted points are connected by line segments from left to right and have coordinates as follows: (1, 1), (2, 2), (3, 2), (4, 0), (5, 2), (6, 3), (7, 3), (8, 1), (9, 1), (10, 2), (11, 4), (12, 1), (13, 1), (14, 0).

D.

01606Year# of Hurricanes

A coordinate system has a horizontal axis labeled Year from 0 to 16 in increments of 2 and a vertical axis labeled Numer of Hurricanes from 0 to 6 in increments of 1. Fourteen plotted points are connected by line segments from left to right and have coordinates as follows: (1, 0), (2, 1), (3, 1), (4, 1), (5, 2), (6, 2), (7, 3), (8, 4), (9, 3), (10, 2), (11, 2), (12, 1), (13, 1), (14, 0).

​d) Discuss the time series plot. Does this graph support the claim of these​ scientists?

The time series plot

▼

does

does not

support the claim that the number of hurricanes has

▼

decreased

increased

as the years progressed.

Answer 1

The data given in the problem is

Year	1	2	3	4	5	6	7	8	9	10	11	12	13	14
# of Hurricanes	1	2	2	0	2	3	3	1	1	2	4	1	1	0

a) If we want to check the frequency of the hurricanes in recent years than we can calculate that "number of years" in which "no or 0 hurricane" occurred is 2.

Similarly, "number of years" in which "1 hurricane" occurred is 5.

"number of years" in which "2 hurricane" occurred is 4.

"number of years" in which "3 hurricane" occurred is 2.

"number of years" in which "4 hurricane" occurred is 1.

# of Hurricanes	0	1	2	3	4
Frequency of occurrence	2	5	4	2	1

A histogram has a horizontal axis labeled "Number of Hurricanes" from 0 to 5 in increments of 1 and a vertical axis labeled from 0 to 6 in increments of 1. The histogram has vertical bars of width 1 starting at the horizontal axis value 0. The heights of the bars are as follows, where the left horizontal axis label is listed first and the height is listed second: 0, 2; 1, 5; 2, 4; 3, 2; 4, 1.So, the first option i.e. A is correct.

The histogram of the above data is given below in picture.

b) As we can see in the histogram the data is unimodal.

For a data to be uniform the frequency of the number of hurricanes needed to be same. Which is not in this case. Now, the maximum frequency of Hurricanes that have occurred is 5 i.e. it is observed that hurricane occurred twice in a year most of the time.Also, if we want to visualize unimodal from the histogram we can see that no two bar are at the same and maximum height.

c) The time series plot for the data is in the picture below.

Year	1	2	3	4	5	6	7	8	9	10	11	12	13	14
# of Hurricanes	1	2	2	0	2	3	3	1	1	2	4	1	1	0

We can see from the above plots that option B is correct i.e.

A coordinate system has a horizontal axis labeled Year from 0 to 16 in increments of 2 and a vertical axis labeled Number of Hurricanes from 0 to 6 in increments of 1. Fourteen plotted points are connected by line segments from left to right and have coordinates as follows: (1, 0), (2, 1), (3, 1), (4, 4), (5, 2), (6, 1), (7, 1), (8, 3), (9, 3), (10, 2), (11, 0), (12, 2), (13, 2), (14, 1).

d) As we see in the time series plot there is no upward or downward pattern we can say that the time series plot does not support the claim that the number of hurricanes have increased in the recent years.