Question

Theoph is a built-in R dataset. The Theoph data frame has 132 rows and 5 columns of data from an experiment on the pharmacokinetics of theophylline. Thus, there are 132 measurements. We are interested in some descriptive statistics related to the conc variable of Theoph. We can access the data directly by using the assignment x <- Theoph$conc (In R use ?Theoph for info on this dataset.) The values of Theoph$conc or x if defined as above are: [1] 0.74, 2.84, 6.57, 10.50, 9.66, 8.58, 8.36, 7.47, 6.89, 5.94, 3.28, 0.00, 1.72 [14] 7.91, 8.31, 8.33, 6.85, 6.08, 5.40, 4.55, 3.01, 0.90, 0.00, 4.40, 6.90, 8.20 [27] 7.80, 7.50, 6.20, 5.30, 4.90, 3.70, 1.05, 0.00, 1.89, 4.60, 8.60, 8.38, 7.54 [40] 6.88, 5.78, 5.33, 4.19, 1.15, 0.00, 2.02, 5.63, 11.40, 9.33, 8.74, 7.56, 7.09 [53] 5.90, 4.37, 1.57, 0.00, 1.29, 3.08, 6.44, 6.32, 5.53, 4.94, 4.02, 3.46, 2.78 [66] 0.92, 0.15, 0.85, 2.35, 5.02, 6.58, 7.09, 6.66, 5.25, 4.39, 3.53, 1.15, 0.00 [79] 3.05, 3.05, 7.31, 7.56, 6.59, 5.88, 4.73, 4.57, 3.00, 1.25, 0.00, 7.37, 9.03 [92] 7.14, 6.33, 5.66, 5.67, 4.24, 4.11, 3.16, 1.12, 0.24, 2.89, 5.22, 6.41, 7.83 [105] 10.21, 9.18, 8.02, 7.14, 5.68, 2.42, 0.00, 4.86, 7.24, 8.00, 6.81, 5.87, 5.22 [118] 4.45, 3.62, 2.69, 0.86, 0.00, 1.25, 3.96, 7.82, 9.72, 9.75, 8.57, 6.59, 6.11 [131] 4.57, 1.17 It is highly recommended that you get your values for x from the assignment defined above above and not from copying the above printout of the data. a. Calculate the sample median of x. b. How many outliers does an R boxplot of x show? c. Calculate the interquartile range of x using R. d. Calculate the sample mean of x. e. Calculate a 10% trimmed mean for x. f. Calculate the sample variance of x. g. Calculate the sample standard deviation of x. h. What proportion of the x values are more than 1 sample standard deviation away from the sample mean i. Calculate the range of x. (one number) j. What number do you get if you sum the values in x? A LI I

Answer 1

Required R-Codes

## Answer using R

x=Theoph$conc
x

# a). To calculate median.
m=median(x)
m

# b). To plot Boxplot
boxplot(x,outline = FALSE)
boxplot.stats(x)

# c).To calculate Interquartile range
Iqr=IQR(x)
Iqr

# d). To calcute sample mean
Mn=mean(x)
Mn

# e).To calculate 10% trimmed mean
Mt=mean(x,trim=10)
Mt

# f). To compute sample variance of x
Sv=var(x)
Sv

# g). To calculate sample standard deviation
Sd=sd(x)
Sd

# h).
length(which(x>(mean(x)+1)))/length(x)*100
## Thus near about 40 % of x values are away from sample mean.

# i). To compure Range of x
R=max(x)-min(x)
R

# j). If we sum the values in x
Sum=sum(x)
Sum

R-Code Outputs generated as follows ;

> x=Theoph$conc
> # a). To calculate median.
> m=median(x)
> m
[1] 5.275
> # b). To plot Boxplot
> boxplot(x)

> boxplot.stats(x)
$stats
[1]  0.000  2.865  5.275  7.140 11.400

$n
[1] 132

$conf
[1] 4.687096 5.862904

$out
numeric(0)

> # c).To calculate Interquartile range
> Iqr=IQR(x)
> Iqr
[1] 4.2625
> # d). To calcute sample mean
>  Mn=mean(x)
>  Mn
[1] 4.960455
> # e).To calculate 10% trimmed mean
> Mt=mean(x,trim=10)
> Mt 
[1] 5.275
> # f). To compute sample variance of x
> Sv=var(x)
> Sv
[1] 8.22152
> # g). To calculate sample standard deviation
> Sd=sd(x)
> Sd
[1] 2.867319
> # h).
> length(which(x>(mean(x)+1)))/length(x)*100
[1] 40.15152
> # i). To compure Range of x
> R=max(x)-min(x)
> R
[1] 11.4
> # j). If we sum the values in x
> Sum=sum(x)
> Sum
[1] 654.78