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.

Question

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.

Options

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

MCQ

Assertion and Reasoning

Solution

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

Explanation:

The mean of x₁, x₂ and x₃ being m indicates that their sum equals 3m by definition. Expanding the expression in the assertion results in (x₁ + x₂ + x₃) − 3m, and substituting 3m into this expression yields 3m − 3m = 0, proving that Assertion (A) is true. Reason (R) accurately outlines this exact algebraic expansion and substitution, making it the correct explanation for Assertion (A).

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Q 1. (g)Q 1. (f)Q 1. (h)

Chapter 18: Mean and Median [For Ungrouped Data Only] - TEST YOURSELF [Page 268]

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Selina Concise Mathematics [English] Class 9 ICSE

Chapter 18 Mean and Median [For Ungrouped Data Only]
TEST YOURSELF | Q 1. (g) | Page 268

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.

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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.

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