Review #1 Question 1

The manager of a men’s store observes the waist size (in inches) of trousers sold yesterday:

32,32,33,40,32,48,34,33,30,28

Calculate the range, variance, and standard deviation of these data. Select the answers equal to or closest to your results.

Range = ?

Variance = ?

Standard Deviation = ?

What percentage of the observations are within 1, 2 and 3 standard deviations of the mean?

Within ±1 standard deviation: =

Within ±2 standard deviation: =

Within ±3 standard deviation: =

How does this compares with what the empirical rule predicts?

Answer

Working with vectors

A vector is a sequence of data elements of thesame basic type - in our case, numbers (a numeric vector). So, use “c()”.

Giving it a name (waist):

waist<-c(32,32,33,40,32,48,34,33,30,28)
View(waist)

It has a skewed distribution!

hist(waist)

All that you need to answer the first part of the question: sd() and mean().

mean<-mean(waist)
sd<-sd(waist)
mean
## [1] 34.2
sd
## [1] 5.750362

Time to construct intervals using ifelse function. Give them a name!

\(1^{st}\) interval

fi<-ifelse((mean-1*sd)<=waist & waist<=(mean+1*sd), 1,0)
View(fi)
## How many observations fit inside the interval?  
## (In other words) How many ones do you have?
sum(fi)
## [1] 7

Don’t forget to calculate the proportion!

prp1st<-sum(fi)/10
prp1st
## [1] 0.7

\(2^{nd}\) interval

si<-ifelse((mean-2*sd)<=waist & waist<=(mean+2*sd), 1,0)
prp2nd<-sum(si)/10
prp2nd
## [1] 0.9

\(3^{rd}\) interval

ti<-ifelse((mean-3*sd)<=waist & waist<=(mean+3*sd), 1,0)
prp3rd<-sum(ti)/10
prp3rd
## [1] 1

Time to compare with what the empirical rule predicts.