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Mathematics

Assertion (A): The mean of x1, x2 and x3 is m. Then the value of (x1 - m) + (x2 - m) + (x3 - m) = 0.

Reason (R): x1 + x2 + x3 = 3m

⇒ (x1 - m) + (x2 - m) + (x3 - m) = (x1 + x2 + x3) - 3m

  1. A is true, but R is false.

  2. A is false, but R is true.

  3. Both A and R are true, and R is the correct reason for A.

  4. Both A and R are true, and R is the incorrect reason for A.

Statistics

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Answer

Given,

Observations = x1, x2 and x3

Mean = m

Number of observations = 3

By formula,

Mean = Sum of observationsNumber of observation\dfrac{\text{Sum of observations}}{\text{Number of observation}}

⇒m=x1+x2+x33⇒3m=x1+x2+x3⇒x1+x2+x3−3m=0⇒(x1−m)+(x2−m)+(x3−m)=0\Rightarrow m = \dfrac{x1 + x2 + x3}{3}\\[1em] \Rightarrow 3m = x1 + x2 + x3\\[1em] \Rightarrow x1 + x2 + x3 - 3m = 0\\[1em] \Rightarrow (x1 - m) + (x2 - m) + (x3 - m) = 0\\[1em]

∴ Both A and R are true, and R is the correct reason for A.

Hence, option 3 is the correct option.

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