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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

What is the mean of the numbers 1,2,3, , 10 with frequencies ^9...

What is the mean of the numbers 1,2,3,…,101,2,3, \ldots, 10 with frequencies 9c0,9c1,9c2,…,9c9{ }^9 c_0,{ }^9 c_1,{ }^9 c_2, \ldots,{ }^9 c_9, respectively?

Options

  1. A1.1×281.1 \times 2^8
  2. B1.2×741.2 \times 7^4
  3. C5.5
  4. D0.55

Correct answer

C. 5.5

Step-by-step solution

 Mean =∑fi⋅xi∑fi=1×9C0+29C1+…+10×9C99C0+9C1+9C2+…+9C9=11×2829=5.5\begin{aligned} \text{ Mean } & =\frac{\sum \mathrm{f}_{\mathrm{i}} \cdot \mathrm{x}_{\mathrm{i}}}{\sum \mathrm{f}_{\mathrm{i}}}=\frac{1 \times{ }^9 \mathrm{C}_0+2{ }^9 \mathrm{C}_1+\ldots+10 \times{ }^9 \mathrm{C}_9}{{ }^9 \mathrm{C}_0+{ }^9 \mathrm{C}_1+{ }^9 \mathrm{C}_2+\ldots+{ }^9 \mathrm{C}_9} \\ & =\frac{11 \times 2^8}{2^9}=5.5\end{aligned}
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