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Question 15.2: Fire Insurance Claims Study Table 15.2 shows the number of f......

Fire Insurance Claims Study

Table 15.2 shows the number of fire insurance claims received by an insurance company in each four-month period from 2008 to 2011.
(See Excel file C15.2 – fire insurance claims.)

Management Question

Calculate a three-period moving average for the number of insurance claims received.

Table 15.2 Number of fire insurance claims received by an insurance company (2008–2011)

2008 2009 2010 2011
Period P1 P2 P3 P1 P2 P3 P1 P2 P3 P1 P2 P3
Claims (y) 7 3 5 9 7 9 12 4 10 13 9 10
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Table 15.3 shows the four-step approach outlined above and the resulting three-period moving average of fire insurance claims received.

The moving average series is a smooth curve, which has ‘ironed out’ the short-term fluctuations.

Table 15.3 Three-period moving average of the number of fire insurance claims received

Period Claims (y) Three-period moving total (centred) Three-period moving average
2008 P1 7 — —
P2 3 7 + 3 + 5 = 15 \frac{15}{3}=5
P3 5 3 + 5 + 9 = 17 \frac{17}{3}=5.67
2009 P1 9 5 + 9 + 7 = 21 \frac{21}{3}=3
P2 7 9 + 7 + 9 = 25 \frac{25}{3}=8.33
P3 9 7 + 9 + 12 = 28 \frac{28}{3}=9.33
2010 P1 12 9 + 12 + 4 = 25 \frac{25}{3}=8.33
P2 4 12 + 4 + 10 = 26 \frac{26}{3}=8.67
P3 10 4 + 10 + 13 = 27 \frac{27}{3}=9
2011 P1 13 10 + 13 + 9 = 32 \frac{32}{3}=10.67
P2 9 13 + 9 + 10 = 32 \frac{32}{3}=10.67
P3 10 — —

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