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The sample mean is always an unbiased estimator of the population mean. This means that the expected value of the sample mean equals the population mean. Therefore, there is no difference between a biased and unbiased estimator of the sample mean - the sample mean itself is already unbiased. The difference is zero. **Key Points:** - The sample mean \(\bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_i\) is an unbiased estimator of the population mean \(\mu\) - \(E[\bar{x}] = \mu\) - No calculation is needed from the data table - this is a conceptual statistical property - The question tests understanding of estimator properties rather than computational skills
Author: Nikitesh Somanthe
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A sample amount of profit for a certain company for the first 15 weeks of the year is given below:
| Weeks | Amount of the Profit($) |
|---|---|
| 1 | 0 |
| 2 | 7,000 |
| 3 | 13,000 |
| 4 | 13,000 |
| 5 | 20,000 |
| 6 | 23,000 |
| 7 | 25,000 |
| 8 | 27,000 |
| 9 | 34,000 |
| 10 | 41,000 |
| 11 | 60,000 |
| 12 | 66,000 |
| 13 | 76,000 |
| 14 | 77,000 |
| 15 | 96,000 |
What is the difference between the biased and an unbiased estimator of the sample mean?
A
0
B
1.0
C
3.2
D
4.6