Question

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

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

Statement (2): For data with n terms, the lower quartile is `((n+1)/4)^(th)` term, if n is odd.

Options

• Both the statements are true.

• Both the statements are false.

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

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

Answer 1

Statement 1 is false, and statement 2 is true.

Explanation:

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+1)/4)^(th)` term, if n is odd

Here, n = 7

\[\text{The lower quantile} = `((n+1)/4)^(th)`

= `((7 + 1)/4)^(th)`

= `(8/4)^(th)`

= 2^{nd term}

= 9

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