Financial Risk Manager Part 1
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The following data represents a sample of daily profit of a sales company for six weeks in a particular year.
| Week | Amount of the Profit($) |
|---|---|
| 1 | 3,800 |
| 2 | 2,800 |
| 3 | 2,700 |
| 4 | 9,900 |
| 5 | 2,600 |
| 6 | 4,300 |
What is the 75% percentile profit?
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A
4,175
B
3,925
C
4,055
D
2,720
Explanation:
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.
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