6. Quintile Example
1. Calculate Quintile-4 from the following data
`85,96,76,108,85,80,100,85,70,95`
Solution:
Arranging Observations in the ascending order, We get :
`70,76,80,85,85,85,95,96,100,108`
Here, `n=10`
`"Quintile"_4 = ((4(n+1))/5)^(th)` value of the observation
`=((4*11)/5)^(th)` value of the observation
`=(8.8)^(th)` value of the observation
`=8^(th)` observation `+0.8[9^(th)-8^(th)]`
`=96+0.8[100-96]`
`=96+0.8(4)`
`=96+3.2`
`=99.2`
2. Calculate Quintile-4 from the following data
`3,23,13,11,15,5,4,2`
Solution:
Arranging Observations in the ascending order, We get :
`2,3,4,5,11,13,15,23`
Here, `n=8`
`"Quintile"_4 = ((4(n+1))/5)^(th)` value of the observation
`=((4*9)/5)^(th)` value of the observation
`=(7.2)^(th)` value of the observation
`=7^(th)` observation `+0.2[8^(th)-7^(th)]`
`=15+0.2[23-15]`
`=15+0.2(8)`
`=15+1.6`
`=16.6`
3. Calculate Quintile-2 from the following data
`4,14,12,16,6,3,1,2,3`
Solution:
Arranging Observations in the ascending order, We get :
`1,2,3,3,4,6,12,14,16`
Here, `n=9`
`"Quintile"_2 = ((2(n+1))/5)^(th)` value of the observation
`=((2*10)/5)^(th)` value of the observation
`=4^(th)` value of the observation
`=3`
4. Calculate Quintile-3 from the following data
`73,70,71,73,68,67,69,72,76,71`
Solution:
Arranging Observations in the ascending order, We get :
`67,68,69,70,71,71,72,73,73,76`
Here, `n=10`
`"Quintile"_3 = ((3(n+1))/5)^(th)` value of the observation
`=((3*11)/5)^(th)` value of the observation
`=(6.6)^(th)` value of the observation
`=6^(th)` observation `+0.6[7^(th)-6^(th)]`
`=71+0.6[72-71]`
`=71+0.6(1)`
`=71+0.6`
`=71.6`
This material is intended as a summary. Use your textbook for detail explanation.
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