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 - Economics

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

SOLUTION

Q₁ = size of 1${\displaystyle {\left(\frac{n+1}{4}\right)}^{\text{th observation}}}$

Q₁ = size of 1${\displaystyle {\left(\frac{15+1}{4}\right)}^{\text{th observation}}}$

Q₁ = Size of 1 ${\displaystyle {\left(\frac{16}{4}\right)}^{\text{th observation}}}$

Q₁ = Size of  1(4)^{th observation} 

Size of the 4^{th observation} = 9

Q₁ = 9

D₄  = Size of 4 ${\displaystyle {\left(\frac{n+1}{10}\right)}^{\text{th observation}}}$

D₄ = Size of 4${\displaystyle {\left(\frac{15+1}{10}\right)}^{\text{th observation}}}$

D₄ = Size of 4${\displaystyle {\left(\frac{16}{10}\right)}^{\text{th observation}}}$

D₄ = Size of 4(1.6)^{th observation}

= Size of 6.4^{th observation}

= Size of 6.4^{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${\displaystyle {\left(\frac{n+1}{100}\right)}^{\text{th observation}}}$

P₂₆ = Size of 26${\displaystyle {\left(\frac{15+1}{100}\right)}^{\text{th observation}}}$

P₂₆ = Size of 26${\displaystyle {\left(\frac{16}{100}\right)}^{\text{th observation}}}$

= 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