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NDA 2 2024 Maths, question 112

Topic: Statistics

Q112

The mean of the series x1,x2,…,xnx_{1},x_{2},\ldots ,x_{n} is x‾\overline{x}. If xnx_{n} is replaced by kk, then what is the new mean?

  1. (a) x‾−xn+k\overline{x}-x_{n}+k
  2. (b) nx‾−x‾+kn\frac{n\overline{x}-\overline{x}+k}{n}
  3. (c) x‾−xn−kn\frac{\overline{x}-x_{n}-k}{n}
  4. (d) nx‾−xn+kn\frac{n\overline{x}-x_{n}+k}{n}Correct answer

Solution.

Answer: (d) nx‾−xn+kn\frac{n\overline{x}-x_{n}+k}{n}

  1. The original total is n x̄.
  2. Replacing xₙ by k changes it to n x̄−xₙ+k, while the number of observations remains n.
  3. Divide by n to obtain option (d).