Emissions of Vehicles to the Environment

Introduction:

Currently on the market there are many options for which cars to buy. The price is based on many factors, the brand, the materials used, the type of car, and the horsepower. Horsepower is a unit of measurement for the power output from a motor. This leads to the aim of the paper. For my Math IA, I plan to determine the relationship between the amount of power a car has (horsepower) and it’s price (MSRP in $). I chose this topic because I personally love cars. I love working on my own car, my friends’, or anyone who needs my help. I was looking to get a different car so this should help me figure out which cars have the best value for performance. Horsepower will be the factor determining “performance” because it will be easiest to calculate alongside the price, and MSRP will be the factor determining price. I chose to not use dealer prices for my data because that would skew the data because of the added fees and such that occur when purchasing a car from a dealership. I wanted to see if the Dodge Demon was actually the best car in terms of performance and price. I intend to scour the internet for cars and their respective performance and price information to determine if there’s a correlation between price and power. I used only new cars to keep the data as controlled as possible.

After compiling the data, I will find the data set’s minimum value, maximum value, first quartile, median, and third quartile. I will then use these values to determine the interquartile range (middle 50%) of the data set as well as any outliers. I will also calculate the standard deviation of the data which tells me the variation or dispersion of it, and construct a boxplot of the data to more clearly indicate the minimum value, maximum value, interquartile range (with the first quartile, median, and third quartile), and the shape of the distribution. I will also be finding Pearson’s Correlation Coefficient (“r”). This will indicate whether my data has a strong, moderate, or weak correlation and whether it is positive or negative.

Information:

To collect this raw data I simply searched the internet for the specs of cars and their MSRP. I chose the cars at random making sure to use regular sedans, luxury sedans, regular SUVs, luxury SUVs, and coupes to get as much variation in my data as I could. I wanted to try and capture as many types of cars as possible. Again, I made sure to only use information from new cars to ensure my data is as precise as possible.

Math Processes:

Finding the minimum value, the first quartile, the median value, the third quartile, the maximum value, interquartile ranges, and outliers.

To find the minimum value, the first quartile, the median value, the third quartile, and the maximum value I used a calculator. I will find these values for both the horsepower data, and the price data set.

Horsepower Set Values:

In the left column I inputted the horsepower data for my chosen automobiles. The calculator yielded the following for the minimum value, the first quartile, the median value, the third quartile, and the maximum value.

• Min (minimum) = 78
• Q1 (first quartile) = 274.5
• Med (median) = 350
• Q3 (third quartile) = 550
• Max (maximum) = 808

This means that the minimum value of the data set was 78 horsepower, the first quartile value was 261.5 horsepower, the median value was 350 horsepower, the third quartile value was 555 horsepower, and the maximum value was 808 horsepower. The first quartile represents the 25th percentile of the data set, so this shows that 25% of cars in this data set have 261.5 horsepower or less. The median is 350, this shows that 50% of cars in this data set have 350 horsepower or less. The third quartile is 555, this shows that 75% of cars in this data set have 555 horsepower or less. Every car represented in this data set has 808 horsepower or less.

The interquartile range (IQR) for this data set is 293.5 horsepower. It represents the middle 50% of the data set. I obtained this value by subtracting the first quartile (Q1) from the third quartile (Q3).

• Q3 - Q1 = IQR
• 555 - 261.5 = 293.5

To determine whether or not any outliers were present in the data set I used the following formulas and inputted them into my calculator:

• Q1 - (1.5 x IQR) for the minimum outlier
• Q3 + (1.5 x IQR) for the maximum outlier
• 261.5 - (1.5 x 293.5) = -178.75
• 555 + (1.5 x 293.5) = 995.25

There are no points in the data set that are below -178.75. That means it’s safe to conclude that there are no minimum outliers. No data points in this set have a value larger than 995.25, from this we can conclude there are no maximum outliers.

Price Set Values:

I repeated the steps above on my calculator, but instead, I inputted the price data set and the calculator yielded the following values for the minimum value, the first quartile, the median value, the third quartile, and the maximum value.

• Min = $13,995
• Q1 = $28,170
• Med = $57,000
• Q3 = $131,950
• Max = $417,826

This means that the minimum value of the price data set was $13,995, the first quartile value was $28,170, the median value was $57,000, the third quartile value was $131,950, and the maximum value was $417,826. The first quartile represents the 25th percentile of the data set, so this shows that 25% of the cars cost below $28,170. The third quartile represents the 75th percentile of the data, so this shows that 75% of the cars cost below 131,950. All of the prices in the set are below 417,826.

The interquartile range for this data set is $103,780. It represents the middle 50% of the data set. I found the IQR by subtracting Q1 from Q3.

• Q3 - Q1 = IQR
• $131,950 - $28,170 = $103,780

To determine whether or not there were any outliers in the data set, I again used the formulas and inputted them into my calculator:

• Q1 - (1.5 x IQR) for the minimum outlier
• Q3 + (1.5 x IQR) for the maximum outlier
• $28,170 - (1.5 x $103,780) = -$127,500
• $131,950 + (1.5 x $103,780) = $287,620

There are no points below -$127,500 that means it’s safe to conclude there are no minimum outliers. There are two values above $287,620: $325,000, and $417,826. From this we can conclude there are no minimum outliers and two maximum outliers.

Drawing Boxplots

Using the minimum value, the first quartile, the median value, the third quartile, and the maximum value, I constructed two boxplots (one for each data set) to more clearly indicate the minimum value, maximum value, interquartile range, and the shape of the distribution.

The boxplot for this data set reveals that the interquartile range is 293.5 horsepower, with the third quartile at 555 horsepower, and the first quartile at 293.5 horsepower. The boxplot displays that the median is 350 horsepower. This whiskers stemming from the boxplot show that the maximum value is 808 horsepower, and the minimum value is 78 horsepower.

The boxplot for this data reveals that the interquartile range is $103,780, with the third quartile at $131,950, and the first quartile at $28,170. The boxplot displays that the median is $57,000. The whiskers stemming from the boxplot show that the maximum value is $261,274 (after the outliers of $325,000 and $417,826 are omitted), and the minimum value is $13,995. The outliers are indicated by marks at the $325,000 and $417,826 points.

Calculating Standard Deviation:

I calculated the standard deviation for the two data sets to describe the spread of the data, and measure the average amount each value deviated from the mean.

The two standard deviations demonstrate that the horsepower data set has a much less variation than the price data set at a standard deviation of 100303.38 in comparison to a standard deviation of 189.6728. This may be related to the outliers of $325,000 and $417,826 present in the price data set which have a greater distance from the mean. The horsepower data set did not have any outliers.

 

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