Question

The first quartile of a data set is 2.5. which statement about the data values is true?

A) three-fourths of the values are less than or equal to 2.5, and one-fourth of the values are greater than or equal to 2.5.



B) Half of the values are less than or equal to 2.5, and half of the values are greater than or equal to 2.5.



C) One-fourth of the values are less than or equal to 2.5, and half of the values are greater than or equal to 2.5.



D) one-fourth of the values are less than or equal to 2.5, and three-fourths of the values are greater than or equal to 2.5.

Answer 1

D) one-fourth of the values are less than or equal to 2.5, and three-fourths of the values are greater than or equal to 2.5.

Explanation:

Answer 2

The correct option is D.

Explanation:

In a data set we have three quartiles and the second quartile is known as median.

First quartile Q₁ divides the data set in 1:3. It means
`(1)/(4)` of the data set are less than or equal to Q₁ and
`(3)/(4)` of the data set are more than or equal to Q₁.

Second quartile Q₂ divides the data set in 1:1. It means
`(1)/(2)` of the data values are less than or equal to Q₂ and
`(1)/(2)` of the data values are more than or equal to Q₂.

Third quartile Q₃ divides the data set in 3:1. It means
`(3)/(4)` of the data values are less than or equal to Q₃ and
`(1)/(4)` of the data values are more than or equal to Q₃.

It is given that first quartile of a data set is 2.5. It means
`(1)/(4)` of the data set are less than or equal to 2.5 and
`(3)/(4)` of the data set are more than or equal to 2.5.

Therefore the correct option is D.