Stats Module A
5 # Summary & IQR Small Cars Medium Cards Large Cars
Minimum 63.0 58.0 39.0
Q1 104.0 79.0 57.5
Median 133.5 102.0 68.0
Q3 147.0 125.0 77.0
Maximum 247.0 169.0 92.0
IQR 43.0 46.0 19.5
Of all cars, based on the center, the largest cares were the safest, the medium cars
were the second safest, and the small cars were the most dangerous. The median of small
cars is 133.5, which is greater than, and therefore more dangerous than, medium’s 102.0
and large’s 68.0. This means that both small and medium cars are more dangerous than
the average car overall, which receives a score of 100; large cars are safer than average,
with a rating significantly below the average 100.
The large cars have the tightest spread, followed by the medium cars and then the
small cars, with the largest spread. The large cars have an IQR of 19.5 and a range of 53;
each quartile has approximately the same range, so there is a uniform spread over the
range, which is much smaller than that of the other cars. The medium cars have a
significantly larger IQR, 46, and range, 111. The fourth quartile is much larger than the
others, yet there are no outliers. The small cars have the largest spread. The IQR is 43,
and although this is slightly less than the IQR of the medium cars, they still have the
largest spread; the range is 184 which is 66% larger than the medium car range.
Additionally, there are three outliers at 221, 246, and 247. The inner quartiles, especially
the third, are smaller than the outer quartiles, further indicating a wide spread beyond the
relatively compact center.
All three of these safety rating plots overlap. 25.0% of large cars are safer than all
medium cars, and 100.0% are safer than the median medium car. 31.3% of large cars are
safer than all small cars, and 100.0% are safer than the median small car. 3.6% of
medium cars are safer than all small cars, and 78.6% are safer than the median small car.
67.9 % of medium cars are more dangerous than all large cars, and 92.9% are more
dangerous than the median large car. 19.2% of small cars are more dangerous than all
medium cars, and 76.9% are more dangerous than the median medium car. 80.8% of
small cars are more dangerous than all large cars, and 96.2% are more dangerous than the
median large car.
These data look at the safety ratings of various cars, categorized by size, to help
determine the insurance rates that should be charged for each type of car. This study was
conducted by the Highway Loss Data Institute from 2000-2001, and published online.
How these data were collected or normalized so that the average rating is 100 is not
The data show that the large cars are the safest by a significant margin. The
median safety rating is 68, well safer than the average, 100; this means that the average
large car was 32% cheaper to repair than the average car, as the interpretation of these
ratings is specified by the data chart. Additionally, the spread is very tight around the
center, meaning that all large cars have better safety ratings than other cars, not just those
around the center. The most dangerous large car, at a rating of 92, is still 8% better than
average and significantly lower than the medians of the other two types of cars, 133.5 and
102, for small and medium respectively. Medium cars and small cars are closely aligned,
yet medium cars are slightly safer. The median of medium cars is at 102, slightly below
average, and has a nearly identical range to the small cars, from 58 to 169; the inner
quartiles, however, is much lower than that of the small cars, [79, 125]. The spread is
much wider than the large cars and about the same as the small cars, with an IQR of 46.
The small cars have the highest median, 133.5, as well as the largest spread. The IQR is
43, with a range of 184 with three outliers, the largest of which is 247. Since small cars
have larger safety ratings plus a larger range, mostly on the more dangerous side of the
median, they are certainly the most dangerous cars to drive.
Based on these data, the company should be advised to give very low rates to the
people with large cars, since the chance of them having an expensive accident is very low
relative to the other cars because of the high safety rating. Thus, medium cars should get
the middle insurance rates, since they are the second most likely to get into accidents that
require expensive repairs. The small cars should have the highest rates, but not be a lot
since they have a similar range to the medium cars. Finally, the Kia Sephia, Mirage, and
Esteem should all be given especially high rates because they are outliers to the
dangerous side in the already dangerous small car class. In conclusion, the large cars are
safer than the medium cars which are safer than the small cars, and the safer cars should
get the lower insurance rates.