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Owner: nnkarma12
Created: Feb 3, 2016
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Auto Safety Nasser

Autosafety report.
Nasser Karmali

Table 1: Data table of the summary results

ColumnnMeanVarianceStd. dev.Std. err.MedianRangeMinMaxQ1Q3
Rating S 26 134.46154 2526.2585 50.261899 9.8571693 133.5 184 63 247 104 147
Rating M 28 104.67857 874.52249 29.572326 5.5886444 102 111 58 169 79 125
Rating L 16 68.125 202.91667 14.244882 3.5612205 68 53 39 92 57.5 77

Figure 2: Boxplot of the Autosafety results

Data analysis:

It is important to first note that the number of data sets for each category (S,M and L) is not the same. Mid size cars has the highest data entry (n=28) followed by the small cars category (n=26) and the large has the least (n=16). Considering the fact that a rating of 100 is the average for all cars, any rating higher than the average will express worse ratings and any ratings under that will express safer ratings.

The box plot shows us that Large car models have the best ratings with the lowest median (M= 68). Small cars were deemed the least safe with a high median of 133.5 followed by the mid size cars with a median of 102. The mean of the cars showed similar results; small cars had the highest mean (M=135) followed by the mid-size cars (M=105) and finally the large cars had the lowest mean ratings (68). This means that the small cars performed 35% worst than the average cars but the large cars performed 32% better on average than the average car.

In terms of variablity of the data, the large cars had the lowest IQR (77-57.5=19.5) whereas the mid size cars had the largest IQR (125-79=46) followed by the the small-size cars with an IQR of 43 (147-104=43).  This shows that the large cars showed consistently better safety ratings compared to the mid size or small cars. It is also of note that the data set between the small and mid size cars overlap which shows some small cars perform better in the safety ratings than the mid size cars even though the means and medians for both groups are different. This can be attributed to the high variability in data for the two groups (IQRs). The small car category also contains three outliers towards the higher ratings which shows three large safety risk cars compared to the average.

Overall, the large cars are consistently safer than the other categories. The small cars are the least safe on average but there is some overlap with the mid-size cars meaning that not all small cars are less safe than the mid size cars and vice versa. Therefore this insurance company should provide low premiums for large cars and higher premiums for mid size and small cars. The three outliers in the small car category should have the highest premium as they are the most prone to accidents.