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 interquartile range?
Other
Community
NNikitesh
A
1,260
B
1,542
C
1,475
D
1,400
Explanation:
Step-by-step calculation:
-
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 Q₁ (first quartile - 25th percentile):
- Position = α × n = 0.25 × 6 = 1.5
- Since 1.5 is not an integer, we average the 1st and 2nd data points
- Q₁ = (2,600 + 2,700) ÷ 2 = 2,650
-
Calculate Q₃ (third quartile - 75th percentile):
- Position = α × n = 0.75 × 6 = 4.5
- Since 4.5 is not an integer, we average the 4th and 5th data points
- Q₃ = (3,800 + 4,300) ÷ 2 = 4,050
-
Calculate IQR (Interquartile Range):
- IQR = Q₃ - Q₁ = 4,050 - 2,650 = 1,400
Why other options are incorrect:
- A (1,260): Incorrect calculation, possibly using wrong quartile positions
- B (1,542): Incorrect calculation, possibly not averaging properly
- C (1,475): Incorrect calculation, possibly using different quartile estimation method
The interquartile range (IQR) measures the spread of the middle 50% of the data and is less sensitive to outliers than the range.
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