Question

Find the quartiles and quartile deviation of the following data: 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

• A. 6.75
• B. 7.25
• C. 5.5
• D. 8

Answer 1

Answer:

A. 6.75

Given data: 17, 2, 7, 27, 15, 5, 14, 8, 10, 24, 48, 10, 8, 7, 18, 28

Ascending order of the given data is: 2, 5, 7, 7, 8, 8, 10, 10, 14, 15, 17, 18, 24, 27, 28, 48

Number of data values = n = 16

Q₁ = (n +1)/4

= 17/4

= 4.25^{th term}

Q₃ = 3(n +1)/4

$=3\times4.25$

= 12.75^{th term}

Q₁ = 4.25^{th term} =(7 + 8)/2

= 7.5

Q₃ = = 12.75^{th term} = (18 + 24)/2

= 21

QD = ( 21 - 7.5)/2

= 13.5/2

= 6.75