The mean of the series x_{1}, x_{2}, \dots, x_{n} is \overline{x}. If x_{n} is replaced by k, then what is the new mean?
- A. \overline{x}-x_{n}+k
- B. \frac{n\overline{x}-\overline{x}+k}{n}
- C. \frac{\overline{x}-x_{n}-k}{n}
- D. \frac{n\overline{x}-x_{n}+k}{n} ✓
Correct Answer: D. \frac{n\overline{x}-x_{n}+k}{n}
Explanation
The sum of the original n observations is n\overline{x}. If the term x_n is removed and replaced by k, the new sum becomes n\overline{x} - x_n + k. The number of observations remains n. Thus, the new mean is \frac{n\overline{x} - x_n + k}{n}.
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