Question

Calculate the mean, standard deviation and co-efficient of variation from the following loss history of a large manufacturing companies workers compensation loss history
a.   Year 1 - $100,000
b.   Year 2 - $125,000
c.   Year 3 - $50,000
d.   Year 4 - $1,250,000 (one large auto accident involving a sales person for $1,150,000)
e.   Year 5 - $85,000
f.   Year 6 - $140,000

Answer 1

Year	Loss Normal	(Loss - Mean Loss )2
1	100000	0
2	125000	625000000
3	50000	2500000000
4	=125000 - 115000* = 100000	0
5	85000	225000000
6	140000	1600000000
Total	600000	4950000000

* Abnormal loss in the year has removed so as to calculate the normal loss scenario.

Mean Loss = Sum of losses / Number of years

                 = 600000 / 6

                 = 100000

Standard Deviation = [(Loss - Mean Loss )2 / n ]1/2

                            = [4950000000 / 6 ]1/2

                            = $ 28722.81

Coefficient of variation = Standard Deviation / Mean

                                = 28722.81 / 100000

                                = 0.2872 Answer

Hope you understand the solution.