3. Decile Example
1. Calculate Deciles-3 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`
`D_3 = ((3(n+1))/10)^(th)` value of the observation
`=((3*9)/10)^(th)` value of the observation
`=(2.7)^(th)` value of the observation
`=2^(nd)` observation ` + 0.7 [3^(rd) - 2^(nd)]`
`=10 + 0.7 [20 - 10]`
`=10 + 0.7 (10)`
`=10 + 7`
`=17`
2. Calculate Deciles-7 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`
`D_7 = ((7(n+1))/10)^(th)` value of the observation
`=((7*9)/10)^(th)` value of the observation
`=(6.3)^(th)` value of the observation
`=6^(th)` observation ` + 0.3 [7^(th) - 6^(th)]`
`=30 + 0.3 [50 - 30]`
`=30 + 0.3 (20)`
`=30 + 6`
`=36`
3. Calculate Deciles-3 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`
`D_3 = ((3(n+1))/10)^(th)` value of the observation
`=((3*11)/10)^(th)` value of the observation
`=(3.3)^(th)` value of the observation
`=3^(rd)` observation ` + 0.3 [4^(th) - 3^(rd)]`
`=80 + 0.3 [85 - 80]`
`=80 + 0.3 (5)`
`=80 + 1.5`
`=81.5`
4. Calculate Deciles-7 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`
`D_7 = ((7(n+1))/10)^(th)` value of the observation
`=((7*11)/10)^(th)` value of the observation
`=(7.7)^(th)` value of the observation
`=7^(th)` observation ` + 0.7 [8^(th) - 7^(th)]`
`=95 + 0.7 [96 - 95]`
`=95 + 0.7 (1)`
`=95 + 0.7`
`=95.7`
This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then
|
