4. Percentile Example
1. Calculate Percentiles-20 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`
`P_20 = ((20(n+1))/100)^(th)` value of the observation
`=((20*9)/100)^(th)` value of the observation
`=(1.8)^(th)` value of the observation
`=1^(st)` observation ` + 0.8 [2^(nd) - 1^(st)]`
`=10 + 0.8 [10 - 10]`
`=10 + 0.8 (0)`
`=10 + 0`
`=10`
2. Calculate Percentiles-75 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`
`P_75 = ((75(n+1))/100)^(th)` value of the observation
`=((75*9)/100)^(th)` value of the observation
`=(6.75)^(th)` value of the observation
`=6^(th)` observation ` + 0.75 [7^(th) - 6^(th)]`
`=30 + 0.75 [50 - 30]`
`=30 + 0.75 (20)`
`=30 + 15`
`=45`
3. Calculate Percentiles-20 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`
`P_20 = ((20(n+1))/100)^(th)` value of the observation
`=((20*11)/100)^(th)` value of the observation
`=(2.2)^(th)` value of the observation
`=2^(nd)` observation ` + 0.2 [3^(rd) - 2^(nd)]`
`=76 + 0.2 [80 - 76]`
`=76 + 0.2 (4)`
`=76 + 0.8`
`=76.8`
4. Calculate Percentiles-75 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`
`P_75 = ((75(n+1))/100)^(th)` value of the observation
`=((75*11)/100)^(th)` value of the observation
`=(8.25)^(th)` value of the observation
`=8^(th)` observation ` + 0.25 [9^(th) - 8^(th)]`
`=96 + 0.25 [100 - 96]`
`=96 + 0.25 (4)`
`=96 + 1`
`=97`
This material is intended as a summary. Use your textbook for detail explanation.
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