Convert The Given Frequency Distribution In Table 2 To A Rel

Convert the given frequency distribution in Table 2 to a relative frequency distribution

This lab involves making an informed decision based on a subjective comparison. We will consider the important issue of car crash fatalities. Car crash fatalities are devastating to the families involved and they often involve lawsuits and large insurance payments. Listed below are the ages of 100 randomly selected drivers who were killed in car crashes. Also given is a frequency distribution of licensed drivers by age.

Table 1: Ages in years of drivers killed in car crashes

Table 2: Age | Number of licensed drivers (in millions)

[Since the exact data from the tables are not provided in the prompt, for the purpose of this paper, assume the following data based on typical distributions]

To convert this frequency distribution into a relative frequency distribution, we need to divide the frequency of each class by the total number of licensed drivers summed across all classes. Assuming the total is 100 million drivers, the relative frequencies are calculated as follows:

For example, for the age group 16-20, the relative frequency is 12 million / 100 million = 0.12. Similarly, for 21-25, it is 15/100 = 0.15, and so on for the other classes.

Creating a Relative Frequency Distribution for Drivers Killed in Car Crashes

Using data from Table 1 (number of fatalities in each age group), we develop a relative frequency distribution based on the same age classifications. For example, suppose the fatalities are distributed as follows:

Summing these numbers, the total fatalities across all age groups is 100. The relative frequency for each group is found by dividing the number of fatalities by the total fatalities. For example, for 16-20 years: 20/100 = 0.20.

Comparison of Relative Frequency Distributions

By comparing the relative frequencies of fatalities with those of licensed drivers, we observe which age groups show disproportionately higher fatalities. For instance, if the 16-20 age group has a relative frequency of 0.20 in fatalities but only 0.12 in licensed drivers, it indicates a higher risk of fatal crashes for this group. Conversely, older age groups with lower fatality proportions relative to their licensed driver proportions suggest comparatively safer driving in those age ranges.

Constructing a Side-by-Side Bar Graph

To visually compare the distributions, create a side-by-side bar graph with age groups on the x-axis. For each age group, place two bars side-by-side: one representing the relative frequency of drivers killed in crashes and the other representing the proportion of licensed drivers. This visual comparison clearly highlights which groups are more prone to fatal crashes.

Report on Relative Frequencies and Insurance Rate Implications

From an insurance perspective, understanding the disparities in fatal crash rates among different age groups informs risk assessment and rate setting. The analysis indicates that younger drivers, particularly those aged 16-20 years, have a notably higher fatality proportion relative to their representation among licensed drivers. Similar trends may be observed in the 21-25 age group, although to a lesser extent.

This elevated risk profile justifies higher auto insurance premiums for these age categories, reflecting the increased likelihood of fatal crashes. Insurance companies incorporate such statistical insights into their pricing strategies to offset potential claims costs. Higher premiums serve both as a risk management tool and as an incentive for safer driving behaviors among high-risk groups.

Furthermore, the data suggest that older drivers, especially those over 50, tend to have lower fatality rates relative to their driver proportions. This trend could be attributed to more cautious driving habits, experienced driving skills, or other factors like health and vehicle safety features.

In conclusion, analyzing the relative frequency of crash fatalities compared with licensed driver distributions supports the practice of differentiated insurance rates based on age-related risk profiles. Such data-driven strategies help insurance companies maintain financial stability while promoting safer driving behaviors across all age groups.

References

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