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 %	Cumulative frequency (cf)
2009	3.75	3.75
2010	3.54	7.29
2011	3.53	10.82
2012	3.62	14.44
2013	3.46	17.9
2014	3.41	21.31
2015	3.49	24.8
2016	3.51	28.31
2017	3.52	31.83
		N = 31.83

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

Therefore,

Q₁ = size of `((31.83 + 1)/4)^{th}` observation

Q₁ = size of `(32.83/4)^{th}` observation

Q₁ = size of 8.21^th observation

size of 8.21^th observation lies in cf 10.82. Thus, quartile value = Year 2011

Q₃ = size of 3`((n + 1)/4)^{th}` observation

Therefore,

Q₃ = size of 3`((31.83 + 1)/4)^{th}` observation

Q₃ = size of 3(8.21)^th observation

Q₃ = size of (3 × 8.21)^th observation

Q₃ = size of 24.63^th observation

size of 24.63^th observation lies in cf 24.8. Hence, quartile value = Year 2015.