Q252 / 270 · NDA 2023 (Phase 2) · Mathematics

If $\bar{X}=20$ is the mean of 10 observations $x_1, x_2 \ldots, x_{10}$, then what is the value of $\sum_{i=1}^{10}\left(\frac{3 x_i-4}{5}\right)$ ?

  • A
    0
  • B
    12
  • Correct answer
    C
    112
  • D
    1012

Solution

Since, $\sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}=10 \times 20=200$ Now, $\frac{1}{5} \sum_{\mathrm{i}=1}^{10}\left(3 \mathrm{x}_{\mathrm{i}}-4\right)$ $=\frac{3}{5} \sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}-\frac{4}{5} \times 10=\frac{3}{5} \times 200-4 \times 2=112$

Hence, the correct answer is option: 'C'.

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