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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Statistics

NDA 2023 · Mathematics · Statistics

If X =20 is the mean of 10 observations x_1, x_2 , x_ 10 , then...

If Xˉ=20isthemeanof10observations\bar{X}=20 is the mean of 10 observationsx_1, x_2 \ldots, x_{10},thenwhatisthevalueof, then what is the value of\sum_{i=1}^{10} (3xi−45)?\left(\frac{3 x_i-4}{5}\right)?

Options

  1. A0
  2. B12
  3. C112
  4. D1012

Correct answer

C. 112

Step-by-step solution

Since, ∑i=110xi=10×20=200\sum_{\mathrm{i}=1}^{10} \mathrm{x}_{\mathrm{i}}=10 \times 20=200 Now, 15∑i=110(3xi−4)=35∑i=110xi−45×10=35×200−4×2=112\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
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