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If variance of ten observations 10,20,30,40,50,....100 is A an

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If variance of ten observations $10, 20, 30, 40, 50, ....100$ is $A$ and variance of ten another observations $22, 42, 62, 82, 102, ......202$ is B, then $\frac{B}{A}$

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If variance of ten observations

10, 20, 30, 40, 50, ....100

A

and variance of ten another observations

22, 42, 62, 82, 102, ......202

is B, then

\frac{B}{A}

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Text solutionVerified

As we have the formula to find the variance of the given observations as follow:-

σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} (x_{i} - \overset{x}{ˉ})^{2}

\overset{x}{ˉ} = 55

σ^{2} = \frac{1}{10} \sum_{i = 1}^{10} (x_{i} - 55)^{2}

= \frac{2}{10} \times 5^{2} (1^{2} + 3^{2} + 5^{2} + 7^{2} + 9^{2})

= 825

A = 825

σ^{2} = \frac{1}{n} \sum_{i = 1}^{n} (x_{i} - \overset{x}{ˉ})^{2}

\overset{x}{ˉ} = 112

σ^{2} = \frac{1}{10} \sum_{i = 1}^{10} (x_{i} - 112)^{2}

= \frac{2}{10} \times 10^{2} (1^{2} + 3^{2} + 5^{2} + 7^{2} + 9^{2})

= 3300

B = 3300

\frac{B}{A} = 4

correct answer is option D

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Question Text	If variance of ten observations $10, 20, 30, 40, 50, ....100$ is $A$ and variance of ten another observations $22, 42, 62, 82, 102, ......202$ is B, then $\frac{B}{A}$
Answer Type	Text solution:1
Upvotes	150