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Created: May 9, 2019
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Descriptive Statistics EbL Report Rafael Centeno
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I analyzed the number of fatalities related to motor vehicle accidents in 2017 by state.

My summary statistics results were:

Summary statistics:


ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3IQRCoef. of var.Mode
Fatalities 51 728.09804 636232.25 797.64168 111.69218 550 3691 31 3722 228 988 760 109.55141 No mode

 The data was obtained from iihs.org. It provided information about the number of fatalities related to motor vehicle accidents in 2017 by state. The data also included the District of Columbia giving a total of 51 results.

Central Tendency:

The average number of fatalities caused by motor vehicle accidents was 728.1 in 2017.

The median of the data collected was 550 deaths, which is almost 200 deaths below the mean number of fatalities. This is due to the wide range of fatalities from the data set. The most exreme numbers from the data set being California 3602, Florida 3112, and Texas 3722. These values are exremely high compared to the mean, this would suggest that this data set will have a right skewed distrubution.

There is no mode according to the summary statistics because no number is repeated throughout the entire data set.

The District of Columbia has the least number of fatalities in this data set, it is extremely low compared to the rest of the data.

Variation:

The standard deviation of the data set is 797.6 deaths, this tells us that the values of the data set are far apart from the mean.

The range of the data is 3691, as suggested by the high standard deviation value, the range is fairly large. This is due to the exreme low value of 31 which is the number of motor vehicle fatalities in the District of Columbia, and the maximum number of fatalities 3722 which represent the fatalities in Texas. Just by looking at from what locations the min. and max. come from, I can tell that the data set is influenced by the population of these states.

 Position: The five number summary is (31, 228, 550, 988, 3722). The IQR is 760, this means that 50% of the data have a range of 760. The other 50% of the data is below 228 or over 988.

I also used a boxplot to analyze the data even further:

 

 The boxplot demonstrated that there were three outliers in the data. California, Florida, and Texas had over 3,000 fatalities due to motor vehicle accidents in 2017. These outliers were over 400% greater than the mean.

Outliers are present, so I have decided to rerun the analysis without the fatalities from California, Florida, and Texas present.

Summary Statistics:

ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3IQRMode
Fatalities 48 556.1875 159304.41 399.12957 57.609391 477 1509 31 1540 207 922 715 No mode

The data set without the exremely high outliers looks a lot different. The mean dropped to 556.2 fatalities, and the Standard deviation dropped almost 50%. The range decreased as well by 59.1%. The IQR only went from 760 to 715, it does not seem like much but the data set definetly deacreased in all areas.

The boxplot without any outliers is still right skewed but only slightly, and there are no more outliers shown after the initial outliers have been removed.

This data set was interesting to me because I had a family member pass away due to a car accident, and I learned that motor vehicle fatalities are not uncommon. I also learned that the number of fatalities from each state may be correlated to the population that state has.

 

Result 1: Summary Stats Motor Vehicle Fatalities   [Info]

Summary statistics:


ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3IQRCoef. of var.Mode
Fatalities51728.09804636232.25797.64168111.692185503691313722228988760109.55141No mode

Result 2: Boxplot 2017 Motor Vehicle Fatalitites   [Info]
Right click to copy

Result 3: Summary Stats Motor Vehicle Fatalities w/out Outliers   [Info]

Summary statistics:


ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3IQRMode
Fatalities48556.1875159304.41399.1295757.6093914771509311540207922715No mode

Result 4: Boxplot Motor Vehicle Fatalities w/ out Outliers   [Info]
Right click to copy

Data set 1. Motor Vehicle Accident Fatalities by State, 2017 D   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87350">Descriptive Statistics EbL Report Rafael Centeno</A>

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