Question

The city of Melonville has a fleet of 350 cars and trucks used by employees to conduct municipal business. Although, the Human Resources Department is diligent in performing background checks before employees are given authority to drive city vehicles, motor vehicle accidents appear to be rising. Skip Wilson, Melonville’s Risk Manager has hired you to help him analyze the current risk situation. He provided you with the following data and would like your assessment for an upcoming presentation he will be making to the Finance Manager.

Data:

Year   Number of Collision Claims        Annual Cost   Average

1                      17                                           $27,500         $1,617.65

2                      11                                           $33,750         $3,068.18

3                      13                                           $41,250         $3,173.08

4                      28                                           $35,000         $1,250.00

5                      39                                           $63,650         $1,632.05

Calculate the following measures and show your work (40 POINTS):

1. Average Frequency for 5 year period
2. Average Severity for 5 year period
3. Probability of loss for 5 year period
4. Range of losses for 5 year period

***I finished that calculations for 1-4 and they are as follows; 1. Avg. Freq: 21.6 2. Avg. Sev: $40,230.00 3. Prob. Loss: 6.17% 4. Range: 28 And I was just curious as to what these numbers meant and your interpretation of them, THANKS!

Answer 1

Hi. You are right. The interpretations and how we are going to use them are more important than the answer itself.

(Here the size of the data sample is less, so the significance is less but would interpret for understanding purpose)

Here,

As a risk manager, I would say to the boss.

" Boss, next year you can expect an average of 21 or 22 collisions that would averagely cost us $40,230. So we need to allocate this on annual risk budget. If we are adding 100 more buses, we can expect an average additional collision of 6 buses. So we need to allocate an additional budget of $11200 (6*average cost per bus). Also, boss! as we are covering insurance policies for a corporate plan of max 100 assets (here buses), I think we can reduce to a minimum plan of insurance up to 50 buses rather than the current plan. So that we can save some dollars on insurance"

This is just the start of something we can interpret we can. Even though next year much less or more collisions can happen, this would simply help us to have a plan for budget or you can use for a different purose. If you can measure, you can interpret and control.

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Bonus!

This might be a little advanced. But will help you to understand why analytics matter.

For example, if we know different factors of 300 buses such as the size of the bus, route travel, driver details, etc. We can use tools such as regression techniques such as linear, logarithmic can be used to find which factors contribute more to the cause of collision.

For example, the probability that a 150 seater bus in the particular route is being an accident on the particular time range is higher. We can change some features and check (here collisions are more sensitive!) or just ask why the particular factors do affect and try work on things. Are we missing something?

Data will enable us to make better decisions. The advance in maths and analytics will help us to increase the prediction accuracy much better.