Question

Solve the following:

Calculate Q₁, D₄, and P₂₆ for the following data.

18, 24, 45, 29, 4, 7, 28, 49, 16, 26, 25, 12, 10, 9, 8

Answer 1

Q₁ = size of 1`((n+1)/4)^"th observation"`

Q₁ = size of 1`((15+1)/4)^"th observation"`

Q₁ = Size of 1 `(16/4)^"th observation"`

Q₁ = Size of  1(4)^th observation 

Size of the 4^th observation = 9

Q₁ = 9

D₄  = Size of 4 `((n+1)/10)^"th observation"`

D₄ = Size of 4`((15+1)/10)^"th observation"`

D₄ = Size of 4`(16/10)^"th observation"`

D₄ = Size of 4(1.6)^th observation

= Size of 6.4^th observation

= Size of 6^th observation + 0.4 (7^th observation – 6^th observation)

= 12 + 0.4 (16 - 12)

= 12 + 0.4 (4)

= 12 + 1.6

= 13.6

D₄ = 13.6

P₂₆ = Size of 26`((n+1)/100)^"th observation"`

P₂₆ = Size of 26`((15+1)/100)^"th observation"`

P₂₆ = Size of 26`(16/100)^"th observation"`

= size of 26 (0.16)^th observation

= Size of 4.16^th observation

= size of 4^th observation + 0.16(5^th observation - 4^th observation)

= 9 + 0.16 (10 - 9)

= 9 + 0.16(1)

= 9 + 0.16

= 9.16

P₂₆ = 9.16