Question

Consider the following data set.

14	27	13	14	15	14	11	13	21	11	25	26	29

a​)

Determine the quartiles for this data.

b​)

Determine the interquartile range for this data.

a​)

The first quartile is

nothing​,

the second quartile is

nothing​,

and the third quartile is

nothing.

​(Type integers or​ decimals.)

b​)

The interquartile range is

nothing.

​(Type an integer or a​ decimal.)

Answer 1

(a)

(i)

Arranging data in ascending order, we get:

11, 11, 13, 13, 14, 14, 14, 15, 21, 25, 26, 27, 29

Bottom half is:

11, 11, 13, 13, 14, 14

The middle of these numbers is:

13.

So,

First Quartile = Q1 = 13

(ii)

n = 13

Second Quartile is (13 + 1)/2th item = 7th item = 14.

So

the Second Quartile = Q2 = 14

(iii)

Upper half is given by:

15, 21, 25, 26, 27, 29

The middle of these numbers is given by

25.5

So,

Third Quartile = Q3 = 25.5

(b)

The Interquartile Range (IQR) is given by:

IQR = Q3 - Q1 = 25.5 - 13 = 12.5

So,

The interquartile range is

12.5