Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
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 25% quantile of the profits?
Other
Community
NNikitesh
A
2750
B
2,700
C
2,650
D
2,600
Explanation:
To find the 25% quantile (first quartile), we need to follow these steps:
-
Sort the data in ascending order:
- 2,600 (Week 5)
- 2,700 (Week 3)
- 2,800 (Week 2)
- 3,800 (Week 1)
- 4,300 (Week 6)
- 9,900 (Week 4)
-
Calculate the position:
- Position = α × n = 0.25 × 6 = 1.5
- Where α = 0.25 (25% quantile) and n = 6 (number of observations)
-
Find the quantile value:
- Since 1.5 is not an integer, we take the average of the values at positions 1 and 2
- Position 1: 2,600
- Position 2: 2,700
- Average = (2,600 + 2,700) ÷ 2 = 2,650
Therefore, the 25% quantile of the profits is $2,650.
Key Points:
- The 25% quantile (Q1) represents the value below which 25% of the data falls
- When the calculated position is not an integer, we interpolate between the two nearest data points
- This method provides a more accurate estimate than simply taking the value at the nearest position
Comments
Loading comments...