Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 84

Question

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.

8408

1374

1872

8879

2459

11413

608

14138

6452

1850

2818

1356

10498

7478

4019

4341

739

2127

3653

5794

8305

A) Compute the mean of the annual sales.

B) Compute the standard deviation of the annual sales.

C) Compute the corresponding z-score of annual sales of $14138 million dollars. According to z-score method is it considered an outlier?

D) Provide a five-number summary.

E) What is the location of the 80th percentile, denoted by L80? What is the 80th percentile?

~Please show work~

8408

1374

1872

8879

2459

11413

608

14138

6452

1850

2818

1356

10498

7478

4019

4341

739

2127

3653

5794

8305

Explanation / Answer

The following question can be solved using R progrmamming. The code and output is given below:

> ## Loading the data:
> x<-c(8408,1374,1872,8879,2459,11413,608,14138,6452,1850,2818,
+ 1356,10498,7478,4019,4341,739,2127,3653,5794,8305)
> ##A.)Finding the mean
> mean(x)

[1] 5170.524
> ##B.) Finding the standard deviation
> sd(x)

[1] 3917.733

> ##C.) Finding the Z-Score of 14138
> z=(14138-mean(x))/sd(x)
> z

[1] 2.288945

> ## Since the z-score lies b/w -3 and 3, it is not an outlier
> ##D.) Five number summary
> summary(x)

Min. 1st Qu. Median Mean 3rd Qu. Max.
608 1872 4019 5171 8305 14138

> ## E.) 80th percentile
> quantile(x,.8)

80%
8408

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