Question

a. Obtain and interpret the quartiles.

Determine the quartiles.

Upper Q 1Q1	equals=	nothing
Upper Q 2Q2	equals=	nothing
Upper Q 3Q3	equals=	nothing

(Type integers or decimals. Do not round.)

Interpret the quartiles. Choose the correct answer below.

A.The quartiles suggest that all of the sharks bear a number of pups between

Upper Q 1Q1

and

Upper Q 3Q3.

B.The quartiles suggest that 25% of the sharks bear a number of pups less than

Upper Q 1Q1,

25% bear a number of pups between

Upper Q 1Q1

and

Upper Q 2Q2,

25% bear a number of pups between

Upper Q 2Q2

and

Upper Q 3Q3,

and 25% bear a number of pups more than

Upper Q 3Q3.

C.The quartiles suggest that the average number of borne pups is

Upper Q 2Q2.

D.The quartiles suggest that 33% of the sharks bear a number of pups less than

Upper Q 1Q1,

33% of the sharks bear a number of pups between

Upper Q 1Q1

and

Upper Q 3Q3,

and 33% of the sharks bear a number of pups more than

Upper Q 3Q3.

b. Determine and interpret the interquartile range.

The interquartile range is

nothing.

(Type an integer or a decimal. Do not round.)

Interpret the interquartile range. Choose the correct answer below.

A.

The approximate difference between each quartile is the IQR.

B.

The data span roughly the IQR.

C.

The average of the first quartile and the third quartile is the IQR.

D.

The number of borne pups in the middle 50% of sharks spans roughly the IQR.

c. Find and interpret the five-number summary.

Determine the five-number summary.

nothing,

nothing,

nothing,

nothing,

nothing

(Type integers or decimals. Do not round. Use ascending order.)

Interpret the five-number summary. Choose the correct answer below.

A.

The distance between the first quartile and the median and the distance between the median and the third quartile have more variation than the distance between the minimum and the first quartile and distance between the third quartile and the maximum.

B.

The distance between the third quartile and the maximum has the greatest variation. The distance between the minimum and the first quartile has the least variation.

C.

The distance between the median and the third quartile has the greatest variation. The distance between the first quartile and the median has the least variation.

D.

The distance between the minimum and the first quartile and distance between the third quartile and the maximum have more variation than the distance between the first quartile and the median and the distance between the median and the third quartile.

d. Identify potential outliers, if any. Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.

A.The potential outlier(s) is(are)

nothing.

(Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.)

B.

There are no potential outliers.

e. Obtain and interpret a boxplot.

Construct the boxplot. Choose the correct graph below.

A.

213

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6, 7, 8, 11. A box encloses the vertical line segments at 6, 7, and 8, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 11. There is a mark at 12. All values are approximate.

B.

213

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6.5, 7, 7.5, 12. A box encloses the vertical line segments at 6.5, 7, and 7.5, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 12. All values are approximate.

C.

213

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6.5, 7, 8, 11. A box encloses the vertical line segments at 6.5, 7, and 8, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 11. There is a mark at 12. All values are approximate.

D.

213

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6, 7, 10, 12. A box encloses the vertical line segments at 6, 7, and 10, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 12. All values are approximate.

Interpret the boxplot. Select all that apply.

A.

There is more variation in the fourth quarter than in any of the other quarters.

B.

The distribution of the data is roughly symmetric.

C.The number of borne pups varies from

33

to

1212.

D.A majority of the sharks bear between

66

and

88

pups.

E.

The potential outlying observation falls far from the rest of the data.

Answer 1

Note: Final answers are highlighted in colour.

a)

Determine the quartiles.

R code for Quantiles

mydata=read.csv("Ans 60/Data.csv",header = TRUE)
quantile(mydata$No.of.Pups)

Output

0% 25% 50% 75% 100%
3 6 7 8 12

Upper Q 1Q1	=	6
Upper Q 2Q2	=	7
Upper Q 3Q3	=	8

Interpret the quartiles. Choose the correct answer below.

A.The quartiles suggest that all of the sharks bear a number of pups between Upper Q 1Q1 and Upper Q 3Q3.

B.The quartiles suggest that​ 25% of the sharks bear a number of pups less than Upper Q 1Q1​, ​25% bear a number of pups between Upper Q 1Q1 and Upper Q 2Q2​, 25% bear a number of pups between Upper Q 2Q2 and Upper Q3Q3​, and​ 25% bear a number of pups more than Upper Q 3Q3.

C.The quartiles suggest that the average number of borne pups is Upper Q 2Q2.

D.The quartiles suggest that​ 33% of the sharks bear a number of pups less than Upper Q 1Q1​, 33% of the sharks bear a number of pups between Upper Q 1Q1 and Upper Q 3Q3​, and​ 33% of the sharks bear a number of pups more than Upper Q 3Q3.

c)

IQR= Q3-Q1= 8-6=2

The interquartile range is 2

Interpret the interquartile range. Choose the correct answer below.

A.The approximate difference between each quartile is the IQR.

B.The data span roughly the IQR.

C.The average of the first quartile and the third quartile is the IQR.

D.The number of borne pups in the middle​ 50% of sharks spans roughly the IQR.

d.

Outlier exists if any value is outside the range ( Q1−1.5×IQR,  Q3+1.5×IQR )

(6-1.5*2 , 8+1.5*2)= (3,11).

There is one value(12) outside the mentioned range.

Identify potential​ outliers, if any. Choose the correct answer below​ and, if​ necessary, fill in the answer box to complete your choice.

A.The potential​ outlier is 12

B.There are no potential outliers.

e. Obtain and interpret a boxplot.

Construct the boxplot. Choose the correct graph below.

A.

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6, 7, 8, 11. A box encloses the vertical line segments at 6, 7, and 8, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 11. There is a mark at 12. All values are approximate.

B.

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6.5, 7, 7.5, 12. A box encloses the vertical line segments at 6.5, 7, and 7.5, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 12. All values are approximate.

C.

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6.5, 7, 8, 11. A box encloses the vertical line segments at 6.5, 7, and 8, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 11. There is a mark at 12. All values are approximate.

D.

213

A boxplot has a horizontal axis labeled from 2 to 13 in increments of 1. There are vertical line segments drawn at the following values: 3, 6, 7, 10, 12. A box encloses the vertical line segments at 6, 7, and 10, and horizontal line segments extend outward from both sides of the box to the vertical line segments at 3 and 12. All values are approximate.

Interpret the boxplot. Select all that apply.

A.There is more variation in the fourth quarter than in any of the other quarters.

B.The distribution of the data is roughly symmetric.

C.The number of borne pups varies from 3 to 12.

D.A majority of the sharks bear between 6 and 8 pups.

E.The potential outlying observation falls far from the rest of the data.