Question

Find out Q₁ and Q₃ using unemployment rates as numerical data:

Year	Unemployment Rate %
2009	3.75
2010	3.54
2011	3.53
2012	3.62
2013	3.46
2014	3.41
2015	3.49
2016	3.51
2017	3.52

Answer 1

Year	Unemployment Rate %
2014	3.41
2013	3.46
2015	3.49
2016	3.51
2017	3.52
2011	3.53
2010	3.54
2012	3.62
2009	3.75
N = 09

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

Q₁ = Size of 1`((9+1)/4)^"th observation"`

Q₁ = Size of 1`((10)/4)^"th observation"`

Q₁ = Size of 1 (2.5)^{th observation}

Q₁ = Size of 2.5^{th observation}

Q₁ = Size of 2^nd observation + 0.5( 3^{rd observation} - 2^{nd observation})

Q₁ = 3.46 + 0.5 (3.49 - 3.46)

Q₁ = 3.46 + 0.5 (0.03)

Q₁ = 3.46 + 0.015 

Q₁ = 3.475

Q₃ = Size of 3`((n+1)/4)^"th observation"`

Q₃ = Size of 3`((9+1)/4)^"th observation"`

Q₃ = Size of 3`((10)/4)^"th observation"`

Q₃ = Size of 3 (2.5)^{th observation}

Q₃ = Size of 7.5^{th observation}

Q₃= Size of 7^th observation + 0.5( 8^{th observation} - 7^{th observation})

Q₃ = 3.54 + 0.5(3.62 - 3.54)

Q₃ = 3.54 + 0.5(0.08)

Q₃ = 3.54 + 0.4

Q₃ = 3.58

Q₁ = 3.475, Q₃ = 3.58