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Mathematics

Data : 9, 11, 15, 19, 17, 13 and 7

Statement (1): For the given data, lower quantile is 11.

Statement (2): For data with n terms, the lower quantile is (n+14)th\Big(\dfrac{n + 1}{4}\Big)^{th} term, if n is odd.

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Measures of Central Tendency

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Answer

Given data : 9, 11, 15, 19, 17, 13 and 7

Arrange the data in ascending order : 7, 9, 11, 13, 15, 17, 19.

For data with n terms, the lower quantile is (n+14)th\Big(\dfrac{n + 1}{4}\Big)^{th} term, if n is odd

Here, n = 7

The lower quantile =(n+14)th=(7+14)th=(84)th=2nd term=9.\text{The lower quantile } = \Big(\dfrac{n + 1}{4}\Big)^{th} \\[1em] = \Big(\dfrac{7 + 1}{4}\Big)^{th} \\[1em] = \Big(\dfrac{8}{4}\Big)^{th} \\[1em] = 2^{\text{nd term}} \\[1em] = 9.

∴ Statement 1 is false, and statement 2 is true.

Hence, option 4 is the correct option.

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