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The variance of 20 observations is $5 .$ If each observatiot multiplied by 2 , then what is the new variance of the resultin:
observations
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observations
Solution:
2713 Upvotes
Verified Answer
The correct answer is:
40
Detailed Method:
Variance $=\frac{\sum \mathrm{d}^{2}}{\mathrm{n}}$
$5=\frac{\sum \mathrm{d}^{2}}{20} \Rightarrow \sum \mathrm{d}^{2}=100$
According to question $\sum\left(\mathrm{d}_{1}\right)^{2}=\sum(2 \mathrm{~d})^{2}=4 \sum \mathrm{d}^{2}=4 \times 100=400$
New variance $=\frac{400}{20}=20$
Shortcut Method:
If each observation is multiplied by 2 New variance $=2^{2} \times 5=20$
Variance $=\frac{\sum \mathrm{d}^{2}}{\mathrm{n}}$
$5=\frac{\sum \mathrm{d}^{2}}{20} \Rightarrow \sum \mathrm{d}^{2}=100$
According to question $\sum\left(\mathrm{d}_{1}\right)^{2}=\sum(2 \mathrm{~d})^{2}=4 \sum \mathrm{d}^{2}=4 \times 100=400$
New variance $=\frac{400}{20}=20$
Shortcut Method:
If each observation is multiplied by 2 New variance $=2^{2} \times 5=20$
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