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 median of the profit?
Other
Community
NNikitesh
A
3,000
B
5,000
C
3,300
D
3,700
Explanation:
Step-by-step explanation:
-
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)
-
Identify the median position:
- Number of observations (n) = 6 (even number)
- For even n, median = average of the two middle values
- Middle positions: position n/2 = 3rd value and position (n/2)+1 = 4th value
-
Calculate the median: $$\text{Median} = \frac{x_3 + x_4}{2} = \frac{2,800 + 3,800}{2} = \frac{6,600}{2} = 3,3004`. Verification:
- The sorted values are: 2,600, 2,700, 2,800, 3,800, 4,300, 9,900
- The two middle values are 2,800 and 3,800
- Their average is (2,800 + 3,800)/2 = 3,300
Why other options are incorrect:
- A. 3,000: This might be an incorrect average or calculation error
- B. 5,000: This is close to the mean (4,350) but not the median
- D. 3,700: This is one of the middle values but not their average
Key concept: The median is the middle value in a sorted dataset. For an even number of observations, it's the average of the two middle values, which makes it less sensitive to outliers (like the 9,900 value) compared to the mean.
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