Question

Suppose that there are 20 numbers in a data set and that they are all different. How many of the values in this data set are between the first quartile and the third quartile?

Answer 1

10 Values

Explanation:

We would use a set of data for illustration

Given the set of numbers:

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20

Since we have an even number of data, the median is in between 10 and 11.

(1,2,3,4,5,6,7,8,9,10),(11,12,13,14,15,16,17,18,19,20)

Lower Half: (1,2,3,4,5,6,7,8,9,10)

• The median of the lower half is in between 5 and 6. So
  `Q_1` is in between 5 and 6.

Upper Half:(11,12,13,14,15,16,17,18,19,20)

• The median of the upper half is in between 15 and 16. So
  `Q_3` is in between 15 and 16.

Therefore, we have the [position of the first and third quartiles as:

1,2,3,4,5,
`Q_1`,6,7,8,9,10,11,12,13,14,15,
`Q_3`,16,17,18,19,20

There are 10 values in between the first and third quartiles.