If for a sample size of 10, ∑ _ i = 1 ^ 10 ( x _ i - 5)^ 2 = 350 and ∑ _ i = 1 ^ 10 ( x _ i - 6) =20 , then the variance is

Correct answer: D. 26 ∑ _ i = 1 ^ 10 ( x _ i - 6) = 20 ⇒ Σ x _ i = 80 ∑ _ i = 1 ^ 10 ( x _ i ^ 2 - 10 x _ i + 25) = 350 ⇒ ∑ _ i = 1 ^ 10 x _ i ^ 2 = 350 + 800 - 250 = 900 Then, variance = (900)/(10) - (8) ^ 2 = 90 - 64 = 26

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Statistics

NTA Abhyas 2020 · Mathematics · Statistics

If for a sample size of 10, ∑ _ i = 1 ^ 10 ( x _ i - 5)^ 2 = 350...

If for a sample size of

10,\mathop{∑}_{i = 1}^{10}\left({x}_{i} - 5\right)^{2} = 350

and

\mathop{∑}_{i = 1}^{10}\left({x}_{i} - 6\right) =20

, then the variance is

Options

A $23$
B $24$
C $25$
D $26$

Correct answer

D. $26$

Step-by-step solution

\mathop{∑}_{i = 1}^{10}\left({x}_{i} - 6\right) = 20 ⇒ Σ{x}_{i} = 80

\mathop{∑}_{i = 1}^{10}\left({{x}_{i}}^{2} - 10{x}_{i} + 25\right) = 350

⇒ \mathop{∑}_{i = 1}^{10}{{x}_{i}}^{2} = 350 + 800 - 250 = 900

Then, variance

= \dfrac{900}{10} - {\left(8\right)}^{2}

= 90 - 64 = 26

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