# mathproj.doc

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```							                  5 Number Summaries and IQR

Small               Mid-size         Large
Minimum   63                  58               39
Q1        104                 79               57.5
Median    133.5               102              68
Q3        147                 125              77
Maximum   247                 169              92
IQR       43                  46               19.5
As can be seen from the data, large cars have a lower median safety rating than the small
and midsize cars. The lower the rating, the safer the car. The large cars’ median rating was 68,
while the small cars’ was 102, and the mid-size cars’ rating 133.5. The smaller the car gets, the
lower the safety rating becomes. The large cars were the only ones to consistently fall below the
average (100). Only about 25% of the small cars and 50% of the mid-size cars compared with
100% of the large cars were below the average (so above average in safety since a low score is
better). The median midsize cars were right at the average, the large far below, and the small far
above.

Moving on to spread and variability, let’s look at the IQR. The small and midsize cars
have similar IQRs (43 and 46 respectively, while the large cars have a much lower IQR (19.5).
so not only do large cars have the best safety ratings, but they also have ratings more
concentrated around the median. The scores are less spread out, and more stable. The small and
midsize cars have much more variable scores, and are therefore much more unpredictable. The
small cars also have outliers. These numbers are abnormally high (in other words abnormally
“unsafe”). They are at 221,246, and 227. There is an overlap of all the data from 63 to 92 (the
small cars’ minimum to the large cars’ maximum). There is greater overlap of the small and
midsize cars. They overlap from the rating values of 63 to 169. Nearly 100% of the midsize data
falls within the small cars data. About 75% of the large car data falls within the data of the small
and midsize cars. There is also an approximate 50% overlap of the midsize car data with the
large car data. This shows that 25% of large cars are safer than small or midsize cars. This can be
determined by examining the quartiles.

Using this data, we can work together to best determine how to serve our customers.
Large cars have much better safety ratings, so we should lower this premium. Small and mid-size
cars have similar safety ratings, but it is much higher than the large cars. Therefore we should
keep that premium higher. The small and mid-size premium should be similar, perhaps with the
small a little higher.

Audrey Baker

```
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