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Question: Answered & Verified by Expert
The standard deviation of $\mathrm{n}$ observations $\mathrm{x}_{1}, \mathrm{x}_{2}, \ldots \ldots \mathrm{x}_{\mathrm{n}}$ is $6 .$ The standard deviation of another set of $\mathrm{n}$ observations $\mathrm{y}_{1}$, $\mathrm{y}_{2}$
$\mathrm{y}_{\mathrm{n}}$ is $8 .$ What is the standard deviation of $\mathrm{n}$ observations $\mathrm{x}_{1}-\mathrm{y}_{1}, \mathrm{x}_{2}-\mathrm{y}_{2}, \ldots \ldots . ., \mathrm{x}_{\mathrm{n}}-\mathrm{y}_{\mathrm{n}} ?$
MathematicsStatisticsNDANDA 2006 (Phase 1)
Options:
  • A 10
  • B 7
  • C 14
  • D 2
Solution:
2214 Upvotes Verified Answer
The correct answer is: 2
The standard deviation of n observation $\mathrm{x}_{1}, \mathrm{x}_{2}$, $\mathrm{x}_{\mathrm{n}}$ is 6 and of $\mathrm{y}_{1}, \mathrm{y}_{2}, \ldots \ldots, \mathrm{y}_{n}$ is 8, then the standard
deviation of n observation $\mathrm{x}_{1}-\mathrm{y}_{1}, \mathrm{x}_{2}-\mathrm{y}_{2}, \mathrm{x}_{3}-\mathrm{y}_{3}, \ldots \ldots$
$x_{n}-y_{n}$ is $8-6=2$.

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