Question

Q1. (3 poins total) Each year the EPA doe s an analysis on Estimated e current models of vehicles sold in the United States. The data provided in this example is a subset of this analysis, if you are curious you may access the full data set from the EPAwebsite http://www.fueleconomy.gov/feg/download.shtml. The following graphical display and numerical summary show the variable estimate annual fuel cost of 882 new vehicles. EPA Estimated Annual Fuel Cost of 2017 Vehici 500 1000 1500 2000 2500 3000 3500 Mean Dev DMn. Median 3d Q Max. Cost in Dollars $1815 $459 $650 $1550 $1750 $2100 $3500 (0.5 point) What type of variable is annual fuel cost? Quantitative or Categorical? a. b. (2.5 points) Using the graphical display and numerical summary, thoroughly describe the distribution of estimated annual fuel cost. Include context, shape, center and spread of the data and whether there are any outliers.

Answer 1

a. From the above Five number summary and the information provided,

the variable annual fuel cost is a Quantitative variable.

Since the data is measured in the numbers, the variable is quantitative.

b)

From the above histogram we say that the distribution of annual cost fuel is approximately symmetric to the center(mean)=$1815

The coefficient of skewness is given by:

$S_k=\frac{3(Mean-Median)}{s}$

$S_k=\frac{3(1815-1750)}{459}$

$S_k=\frac{3*65}{459}$

$S_k=\frac{195}{459}$

$S_k=0.4248$

Since the value of coefficient of skewness is very small the shape of the annual fuel is symmetric.

Here Inter quartile range(IQR) =Q3-Q1

=2100-1550

IQR=550

The observation which is below IQR-1.5*Q1 and above IQR+1.5*Q3 is considered as an outliers in the data.

Hence,

IQR-1.5*Q1=550-1.5*1550 and IQR+1.5*Q3 =550+1.5*2100

=550-2325 and =550+3150

=-1775 and =3700

Therefore the observations which is outside the range of (-1775,3700) are outliers.

Hence the data does not have any outlier.