If average of 20 observations x1 x2 x20 is y then…

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If average of 20 observations x1, x2, . . . . . x20 is y, then the average of x1 – 101, x2 – 101, x3 – 101, . . . . . x20 – 101 is :

  1. A. y – 20
  2. B. y – 101
  3. C. 20y
  4. D. 101y

Answer: Option B

Here is complete explanation of If average of 20 observations x1 x2 x20 is y then….

Solution(By ExamCraze Team)

According to the question,
$$eqalign{ & Rightarrow frac{{{x_1} + {x_2} + {x_3} + {x_4} + .... + {x_{20}}}}{{20}} = y cr & Rightarrow {x_1} + {x_2} + {x_3} + {x_4} + .... + {x_{20}} = 20y cr} $$

$$ = frac{{{x_1} - 101 + {x_2} - 101 + {x_3} - 101 + {x_4} - 101 + .... + {x_{20}} - 101}}{{20}}$$
$$ = frac{{left( {{x_1} + {x_2} + {x_3} + {x_4} + .... + {x_{20}}} right) - 20 times 101}}{{20}}$$
$$eqalign{ & = frac{{20y - 20 times 101}}{{20}} cr & = y - 101 cr} $$

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