2. Quartile Example
1. Calculate Quartile-1 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`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(9/4)^(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`
2. Calculate Quartile-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`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*9)/4)^(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 Quartile-3 from the following data
`3,13,11,15,5,4,2`
Solution:
Arranging Observations in the ascending order, We get :
`2,3,4,5,11,13,15`
Here, `n = 7`
`Q_3 = ((3(n+1))/4)^(th)` value of the observation
`=((3*8)/4)^(th)` value of the observation
`=6^(th)` value of the observation
`=13`
4. Calculate Quartile-1 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`
`Q_1 = ((n+1)/4)^(th)` value of the observation
`=(11/4)^(th)` value of the observation
`=(2.75)^(th)` value of the observation
`=2^(nd)` observation ` + 0.75 [3^(rd) - 2^(nd)]`
`=76 + 0.75 [80 - 76]`
`=76 + 0.75 (4)`
`=76 + 3`
`=79`
This material is intended as a summary. Use your textbook for detail explanation.
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