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in Economics by (60.1k points)

Calculate Q1, Q2 and Q3 from the following data:

22, 26, 14, 30, 18, 11, 35, 41, 12, 32.

1 Answer

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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:

Q= Size of \((\frac{N + 1}{2})^{th}\) item

Q= Size of \((\frac{ 10 + 1}{4})^{th}\) item

= Size of \((\frac{11}{2})^{th}\) item

Q= 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

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