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AP EAMCET201921 Apr 2019Evening ShiftMathematicsStatisticsActual

The standard deviations of x i i = 1 , 2 , … . 10 and y i i = 1 , … 10 are respectively a and b . x ¯ , y ¯ are the means of these two sets of observations respectively. If z i = x i - x ¯ y i - y ¯ and ∑ i = 1 10 z i = c , then the standard deviation of the observations x i - y i , i = 1 , 2 , … 10 is

Options

  1. Aa 2 + b 2 + c 5
  2. Ba 2 + b 2 - c 5
  3. Ca 2 + b 2 - c 2 5
  4. Da 2 + b 2 + c 2 5

Correct answer

B. a 2 + b 2 - c 5

Step-by-step solution

It is given that, z i = x i - x ¯ y i - y ¯ And ∑ i = 1 10 z i = c Rewrite the above equation. ∑ i = 1 10 x i - x ¯ y i - y ¯ = c ⇒   ∑ i = 1 10 x i y i - x i y ¯ - x ¯ y i + x ¯ · y ¯ = c ⇒   ∑ i = 1 10 x i y i - ∑ i = 1 10 x i y ¯ - ∑ i = 1 10 x ¯ y i + ∑ i = 1 10 x ¯ · y ¯ = c ⇒   ∑ i = 1 10 x i y i - 10 x ¯ · y ¯ - 10 x ¯ · y ¯ + 10

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