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Mathematics

Assertion (A): The number of goals scored by a football team in a series of matches are 3, 1, 0, 7, 5, 3, 3, 4, 1, 2, 0, 2

The median of the data is 2.5.

Reason (R): Median of an ungrouped data is the variate which has maximum frequency.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Measures of Central Tendency

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Answer

Given goals: 3, 1, 0, 7, 5, 3, 3, 4, 1, 2, 0, 2

Arrange the data in ascending order: 0, 0, 1, 1, 2, 2, 3, 3, 3, 4, 5, 7

There are 12 values (even).

By formula,

Median =n2th observation+(n2+1)th observation2=122th observation+(122+1)th observation2=6th observation+(6+1)th observation2=6th observation+7th observation2=(2 + 3)2=52=2.5.\text{Median }= \dfrac{\dfrac{n}{2}\text{th observation} + \Big(\dfrac{n}{2} + 1\Big)\text{th observation}}{2}\\[1em] = \dfrac{\dfrac{12}{2}\text{th observation} + \Big(\dfrac{12}{2} + 1\Big)\text{th observation}}{2}\\[1em] = \dfrac{6\text{th observation} + (6 + 1)\text{th observation}}{2}\\[1em] = \dfrac{6\text{th observation} + 7\text{th observation}}{2}\\[1em] = \dfrac{(2 + 3)}{2} = \dfrac{5}{2} \\[1em] = 2.5.

∴ Assertion (A) is true.

The median is a measure of central tendency that splits your ordered data into two equal parts—half the observations lie below it, and half lie above it.

∴ Reason (R) is false.

∴ Assertion (A) is true, but Reason (R) is false.

Hence, option 1 is the correct option.

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