Calculation of Q1:
Q1 = Size of \((\frac{ N + 1}{2})^{th}\) item = Size of \((\frac{ 10 + 1}{4})^{th}\) item
= Size of \((\frac{11}{4})^{th}\) item = Size of 2.75th item
= 2nd item + 0.75th item
i.e., 2nd item + 0.75th ( 3rd item – 2nd item )
Q1 = 12 + 0.75 ( 14 – 12 ) = 12 + 0.75 (2) = 12 + 1.5
Q1 = 13.5
Calculation of Q2:
Q2 = Size of \((\frac{N + 1}{2})^{th}\) item
Q2 = Size of \((\frac{ 10 + 1}{4})^{th}\) item
= Size of \((\frac{11}{2})^{th}\) item
Q2 = Size of 5.5th item
i.e., value of \((\frac{5^{th} + 6^{th}}{2})\) item
Q2 = = \(\frac {40 + 45}{2}\) = \(\frac{85}{2}\)
Q2 = 42.5
Calculation of Q3:
Q3 = Size of 8.25th item
Q3 = 8th item + 0.25( 9th item – 8th item )
Q3 = 32 + 0.25 (35 – 32) = 32 + 0.25 (3) = 32 + 0.75
Q3 = 32.75