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Mathematics

Assertion (A): The mean of first 9 natural numbers is 4.5.

Statement 2: Mean = Sum of all observationsTotal number of observations\dfrac{\text{Sum of all observations}}{\text{Total number of observations}}

  1. (A) is true, (R) is false.

  2. (A) is false, (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).

Measures of Central Tendency

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Answer

First 9 natural numbers = 1, 2, 3, 4, 5, 6, 7, 8, 9

By formula,

Mean =Sum of all observationsTotal number of observations=1+2+3+4+5+6+7+8+99=459=5.\Rightarrow \text{Mean } = \dfrac{\text{Sum of all observations}}{\text{Total number of observations}}\\[1em] = \dfrac{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9}{9}\\[1em] = \dfrac{45}{9}\\[1em] = 5.

∴ (A) is false, (R) is true.

Hence, option 2 is the correct option.

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