Financial Risk Manager Part 1

Explanation

To calculate the 75th percentile for this dataset:

Step 1: Sort the data in ascending order:

• Week 5: $2,600
• Week 3: $2,700
• Week 2: $2,800
• Week 1: $3,800
• Week 6: $4,300
• Week 4: $9,900

Step 2: Determine the position for the 75th percentile For a dataset with n=6 observations, the position for the p-th percentile is calculated as: Position = (n + 1) × p = (6 + 1) × 0.75 = 7 × 0.75 = 5.25

Step 3: Interpolate between the 4th and 5th observations The position 5.25 means we need to interpolate between:

• 4th observation: $3,800
• 5th observation: $4,300

Step 4: Calculate the weighted average q₇₅ = (1 - 0.25) × 3,800 + 0.25 × 4,300 = 0.75 × 3,800 + 0.25 × 4,300 = 2,850 + 1,075 = 4,175

Therefore, the 75th percentile profit is $4,175.