If average of 20 observations x1, x2, . . . . . x20 is y, then the average of x1 - 101, x2 - 101, x3 - 101, . . . . . x20 - 101 is :
A. y - 20
B. y - 101
C. 20y
D. 101y
Answer: Option B
Solution(By Examveda 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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