5. Octile Example
1. Calculate Octile-5 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`
`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation
`=((5*11)/8)^(th)` value of the observation
`=(6.875)^(th)` value of the observation
`=6^(th)` observation `+0.875[7^(th)-6^(th)]`
`=85+0.875[95-85]`
`=85+0.875(10)`
`=85+8.75`
`=93.75`
2. Calculate Octile-2 from the following data
`10,50,30,20,10,20,70,30`
Solution:
Arranging Observations in the ascending order, We get :
`10,10,20,20,30,30,50,70`
Here, `n=8`
`"Octile"_2 = ((2(n+1))/8)^(th)` value of the observation
`=((2*9)/8)^(th)` value of the observation
`=(2.25)^(th)` value of the observation
`=2^(nd)` observation `+0.25[3^(rd)-2^(nd)]`
`=10+0.25[20-10]`
`=10+0.25(10)`
`=10+2.5`
`=12.5`
3. Calculate Octile-5 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`
`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation
`=((5*11)/8)^(th)` value of the observation
`=(6.875)^(th)` value of the observation
`=6^(th)` observation `+0.875[7^(th)-6^(th)]`
`=85+0.875[95-85]`
`=85+0.875(10)`
`=85+8.75`
`=93.75`
4. Calculate Octile-5 from the following data
`69,66,67,69,64,63,65,68,72`
Solution:
Arranging Observations in the ascending order, We get :
`63,64,65,66,67,68,69,69,72`
Here, `n=9`
`"Octile"_5 = ((5(n+1))/8)^(th)` value of the observation
`=((5*10)/8)^(th)` value of the observation
`=(6.25)^(th)` value of the observation
`=6^(th)` observation `+0.25[7^(th)-6^(th)]`
`=68+0.25[69-68]`
`=68+0.25(1)`
`=68+0.25`
`=68.25`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
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