Question

Consider the following sample:

120, 94, 88, 67, 82, 106, 140, 102, 87, 99, 106, 86, 105, 93

a) Calculate the sample mean and the sample standard deviation

b) Calculate the sample range. What does it mean?

c) What is the mode of the data distribution?

d) Construct a box plot and interpret the result.

e) Identify the 45th percentile and interpret the result.

f) If the two largest data from above data distribution is removed, then what will be its impact on the result that you have obtained in (a)?

Answer 1

> # storing the sample data in variable x

 > x <- c(120,94,88,67,82,106,140,102,87,99,106,86,105,93)  > #a) Calculating the sample mean and sample standard deviation of the data > mean(x) [1] 98.21429 > sd(x) [1] 17.68171 > #b) calculating the sample range > range(x) [1] 67 140 > max(x)-min(x) [1] 73 

#sample range indicating the spread of maximum and minimum value, here the maximum value is 140 and minimum value is 67

# c) calculating the mode of the distribution

 > # Create the function. > getmode <- function(v) { +  uniqv <- unique(v) +  uniqv[which.max(tabulate(match(v, uniqv)))] + }  > print(getmode(x)) [1] 106 # hence, the mode is 106 > #d) constructing the boxplot > boxplot(x,main = "boxplot of x") 

# from the boxplot we can say that the data is symmetrically distributed,
#with one outlier whose value is 140.

 > #e) computing the 45th percentil > quantile(x,probs = 0.45)  45% 93.85 # the 45th percentile is 93.85, this means that 45% of data lies below 93.85 > # removing two largest data from x > #removing the first largest value >  x1 <-x[-which.max(x)] > #removing the second largest value >  x2 <- x1[-which.max(x1)] > print (x2)  [1] 94 88 67 82 106 102 87 99 106 86 105 93 > mean(x2) [1] 92.91667 > sd(x) [1] 17.68171

# after removing the two maximum value mean of new data is decrease while
# standard deviation remain same.