Question

the third decile for the numbers 15,10,20,25,18,11,9,12 is ?

Answer 1

Deciles ( Measures of Positions ):
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The deciles are the values ( nine in numbers ) of the variable that divide an ordered data set into 10 equal parts so that each equal part represents 1/10 of the sample .

* Deciles are denoted by D1 , D2 , ....., D9 , D10.

Finding Deciles for ungrouped Data :
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First arrange the data according to the magnitude of the values

m th decile = Dm = m × [( n+1)/10 ] th value --------(1)

Where
m = 1 , 2 , 3 ......., 9

n = total observations in the data

* Data given 15 , 10 , 20 , 25, 18 , 11 , 9 ,12

Arrenging the data in ascending order we get

9 , 10 , 11 , 12 , 15 , 18 , 20 , 25

Number of observations = n = 8

According to the equation (1),

Third decile=( D 3) = 3 × [ ( 8+ 1 ) / 10 ] th value

= 3 × ( 9/10 ) th value

= 27/10 th value

D 3 = 2.7 th value

The value of third decile can be calculated as

2 nd observation + { 3 rd observation - 2 nd observation } × 0.7

As 2nd observation is 10 and 3rd observation is 11.

Therefore

Third decile = D 3 = 10 + { 11 - 10 } × 0.7

= 10 + 0.7

= 10. 7

Required D3 = 10.7

I hope this will useful to u.