If the mean of 20 observations, namely x_1,x_2,x_3, ,x_ 20 is 1·414 , then what is the value of ∑_ i=1 ^ 20 100(2x_i+4) ?

Correct answer: D. 13656 Given the mean of 20 observations is 1.414 . (1)/(20) ∑_ i=1 ^ 20 x_i = 1.414 ∑_ i=1 ^ 20 x_i = 20 × 1.414 = 28.28 We need to find the value of ∑_ i=1 ^ 20 100(2x_i + 4) . ∑_ i=1 ^ 20 100(2x_i + 4) = 100 (2 ∑_ i=1 ^ 20 x_i + ∑_ i=1 ^ 20 4 ) = 100 (2(28.28) + 20 ×4 ) = 100 (56.56 + 80) = 100 (136.56) = 13656

NDA 2026

Exam: NDA
Year: 2026
Subject: Mathematics
Chapter: Statistics

NDA 2026 · Mathematics · Statistics

If the mean of 20 observations, namely x_1,x_2,x_3, ,x_ 20 is 1·414...

If the mean of

20

observations, namely

x_1,x_2,x_3,\ldots,x_{20}

1\cdot414

, then what is the value of

\sum_{i=1}^{20}100(2x_i+4)

Options

A $24168$
B $20828$
C $15248$
D $13656$

Correct answer

D. $13656$

Step-by-step solution

Given the mean of

20

observations is

1.414

\dfrac{1}{20} \sum_{i=1}^{20} x_i = 1.414

\sum_{i=1}^{20} x_i = 20 \times 1.414 = 28.28

<br><br>We need to find the value of \sum_{i=1}^{20} 100(2x_i + 4)

\sum_{i=1}^{20} 100(2x_i + 4) = 100 \left(2 \sum_{i=1}^{20} x_i + \sum_{i=1}^{20} 4 \right)

= 100 \left(2(28.28) + 20 \times4 \right)

= 100 (56.56 + 80)

= 100 (136.56) = 13656

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