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Mathematics

Assertion (A): The median of : 25, 16, 26, 32, 31, 19, 28, 35 is 31.

Reason (R): To find median of the given data, the variate: x1, x2 , x3, ……………, xn needs to be arranged in ascending or descending order.

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

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Answer

A is false, R is true.

Explanation

On arranging the the given set of data in ascending order of magnitude, we get:

16, 19, 25, 26, 28, 31, 32, 35.

Number of observations, n = 8 (even)

Median = value of (n2)thterm+value of (n2+1)thterm2\dfrac{\text{value of }\Big(\dfrac{n}{2}\Big)^{th} \text{term} + \text{value of }\Big(\dfrac{n}{2} + 1\Big )^{th} \text{term} }{2}

= 82th+(82+1)th2\dfrac{\dfrac{8}{2}^{th} + (\dfrac{8}{2} + 1)^{th}}{2}

= 4th+(4+1)th2\dfrac{4^{th} + (4 + 1)^{th}}{2}

= 4th+5th2\dfrac{4^{th} + 5^{th}}{2}

= 26+282\dfrac{26 + 28}{2}

= 542\dfrac{54}{2}

= 27

∴ Assertion (A) is false.

To find median of the given data, the variate: x1, x2 , x3, ……………, xn needs to be arranged in ascending or descending order.

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.

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