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Mathematics

Assertion (A): In a frequency distribution the class marks are 5, 15 and 25. The corresponding class-intervals are 5 - 15 and 15 - 25.

Reason (R): ∵ 15−52=5\dfrac{15-5}{2} = 5 and 25−152=5\dfrac{25-15}{2}=5
∴ Class-intervals are : (5 - 5) - (5 + 5), (15 - 5) - (15 + 5) and (25 - 5) - (25 + 5)

  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

Class mark = lower limit + upper limit2\dfrac{\text{lower limit + upper limit}}{2}

For the first interval (5, 15):

Lower limit = 5, Upper limit = 15.

Class mark = L1+U12\dfrac{{L1 + U1}}{2}

= 5+152\dfrac{{5 + 15}}{2}

= 202\dfrac{20}{2}

= 10

For the second interval (15, 25):

Lower limit = 15, Upper limit = 25.

Class mark = L2+U22\dfrac{{L2 + U2}}{2}

= 15+252\dfrac{15 + 25}{2}

= 402\dfrac{40}{2}

= 20

According to Assertion, the class mark are 5, 15 and 25, which are incorrect.

∴ Assertion (A) is false.

For the class mark 5, the interval is [5 - 5, 5 + 5] = (0, 10).

For the class mark 15, the interval is [15 - 5, 15 + 5] = (10, 20).

For the class mark 25, the interval is [25 - 5, 25 + 5] = (20, 30).

∴ Reason (R) is true.

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

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