Financial Risk Manager Part 1
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On Tuesday, an insurance company receives a total of 10 claims for automobile policies. After the first-round assessment, it's found that the mean claim amount of the 10 claims is $426 while the standard deviation is 112. On Tuesday, the chief claims analyst authorizes the removal of one of the claims for $545 from the list on grounds that it's fraught with fraud. Compute the standard deviation for the remaining set of 9 claims.
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TTanishq
A
110.2
B
12145.2
C
421.8
D
420
Explanation:
Calculation Steps
Step 1: Calculate the total sum of original claims
- Mean =
$426, n = 10 - Total sum ∑x = 426 × 10 = 4,260
Step 2: Calculate new total after removing fraudulent claim
- Remove claim of
$545 - New ∑x = 4,260 - 545 = 3,715
- New mean = 3,715 ÷ 9 =
$412.8
Step 3: Calculate sum of squares for original claims
Using the formula: s² = 1/(n-1)[∑x² - n·x̄²]
- 112² = 1/9[∑x² - 10 × 426²]
- 12,544 = 1/9[∑x² - 1,814,760]
- ∑x² = 12,544 × 9 + 1,814,760 = 1,927,656
Step 4: Calculate sum of squares after removing fraudulent claim
- Remove 545² = 297,025
- New ∑x² = 1,927,656 - 297,025 = 1,630,631
Step 5: Calculate variance for remaining 9 claims
- s² = 1/(9-1)[1,630,631 - 9 × 412.8²]
- s² = 1/8[1,630,631 - 9 × 170,403.84]
- s² = 1/8[1,630,631 - 1,533,634.56]
- s² = 1/8 × 96,996.44 = 12,124.555
Step 6: Calculate standard deviation
- s = √12,124.555 ≈ 110.2
Therefore, the standard deviation for the remaining 9 claims is approximately $110.2
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