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ICSE Class 10 Mathematics Question 41 of 49

Multiple-Choice Questions — Question 41

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Question 41

Assertion (A) : For a collection of 11 arrayed data, the median is the middle number.

Reason (R) : For the data 5, 9, 7, 13, 10, 11, 10, the median is 13.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. Both A and R are true.

Answer

For 11 arrayed data.

Median = n+12\dfrac{n + 1}{2} th term

= 11+12\dfrac{11 + 1}{2}

= 6th term, which will be the middle term.

∴ For a collection of 11 arrayed data, the median is the middle number.

∴ Assertion (A) is true.

Numbers = 5, 9, 7, 13, 10, 11, 10

Arranging in ascending order, we get :

5, 7, 9, 10, 10, 11, 13.

n = 7, which is odd.

Median = n+12=7+12=82\dfrac{n + 1}{2} = \dfrac{7 + 1}{2} = \dfrac{8}{2} = 4th term = 10.

∴ Reason (R) is false.

Hence, Option 3 is the correct option.