Materi : Data dan Statistika
Rumus Quartil, Desil, Persentil
[ Q,D,P ]n = Tb + ( [ Q,D,P ]n - fks )/f( K( [ Q,D,P ]n) ) . pk
Tb = Tepi Bawah [ - 0,5 ] biasanya
fks = frekuensi kumulatif sebelum
f( K( [ Q,D,P ]n) ) = frekuensi kelas quartil,desil, atau persentil
pk = panjang kelas
____________________________/
Banyak Data = 40 data
Jumlah Data :
3(42) + 4(47) + 11(52) + 15(57) + 7(62)
= 126 + 188 + 572 + 855 + 434
= 314 + 1.427 + 434
= 748 + 1.427
= 2.175
Maka Mean = 2.175/40 = 54,375
Median ( Q2 )
Q2 = 2/4n = 2/4(40) = X20 => K( 55 - 59 ) [ X19 - 33 ]
Tb = 54,5, pk = [ 55,56,57,58,59 ] = 5
frekuensi kumulatif sebelum = 18 [ 3,4,11 ]
f( K(Q2) ) = 15
---
Q2 = 54,5 + ( 20 - 18 )/15 . 5
Q2 = 54,5 + 2/18 . 5
Q2 = 54,5 + 5/9
Q2 = 54,5 + 0,555..
Q2 = 55,0555..
Modus => K( 55 - 59 ), dengan frekuensi sebanyak 15 data.
Q3 = 3/4n = 3/4(40) = X30 => K( 55 - 59 ) [ X19 - 33 ]
Tb = 54,5, pk = 5, f( K(Q3) ) = 15, fks = 18
Q3 = 54,5 + ( 30 - 18 )/15 . 5
Q3 = 54,5 + 12/15 . 5
Q3 = 54,5 + 12/3
Q3 = 54,5 + 4
Q3 = 58,5
D4 = 4/10(40) = X16 => K( 50 - 54 ) [ X8 - 18 ]
Tb = 49,5, pk = 5, fks = 7, f( K(D4) ) = 11
D4 = 49,5 + ( 16 - 7 )/11 . 5
D4 = 49,5 + 9/11 . 5
D4 = 49,5 + 45/11
D4 = 49,5 + 4,0909..
D4 = 53,5909..
P65 = 65/100(40) = 13/20(40) = X26 => K( 55 - 50 ) [ X19 - 33 ]
Tb = 54,5, pk = 5, f( K(P65) ) = 15, fks = 18
P65 = 54,5 + ( 26 - 18 )/15 . 5
P65 = 54,5 + 8/3
P65 = 54,5 + 2,666..
P65 = 57,1666..
----
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]
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Materi : Data dan Statistika
Rumus Quartil, Desil, Persentil
[ Q,D,P ]n = Tb + ( [ Q,D,P ]n - fks )/f( K( [ Q,D,P ]n) ) . pk
Tb = Tepi Bawah [ - 0,5 ] biasanya
fks = frekuensi kumulatif sebelum
f( K( [ Q,D,P ]n) ) = frekuensi kelas quartil,desil, atau persentil
pk = panjang kelas
____________________________/
Banyak Data = 40 data
Bagian A
Jumlah Data :
3(42) + 4(47) + 11(52) + 15(57) + 7(62)
= 126 + 188 + 572 + 855 + 434
= 314 + 1.427 + 434
= 748 + 1.427
= 2.175
Maka Mean = 2.175/40 = 54,375
Bagian B
Median ( Q2 )
Q2 = 2/4n = 2/4(40) = X20 => K( 55 - 59 ) [ X19 - 33 ]
Tb = 54,5, pk = [ 55,56,57,58,59 ] = 5
frekuensi kumulatif sebelum = 18 [ 3,4,11 ]
f( K(Q2) ) = 15
---
Q2 = 54,5 + ( 20 - 18 )/15 . 5
Q2 = 54,5 + 2/18 . 5
Q2 = 54,5 + 5/9
Q2 = 54,5 + 0,555..
Q2 = 55,0555..
Bagian C
Modus => K( 55 - 59 ), dengan frekuensi sebanyak 15 data.
Bagian D
Q3 = 3/4n = 3/4(40) = X30 => K( 55 - 59 ) [ X19 - 33 ]
Tb = 54,5, pk = 5, f( K(Q3) ) = 15, fks = 18
---
Q3 = 54,5 + ( 30 - 18 )/15 . 5
Q3 = 54,5 + 12/15 . 5
Q3 = 54,5 + 12/3
Q3 = 54,5 + 4
Q3 = 58,5
Bagian E
D4 = 4/10(40) = X16 => K( 50 - 54 ) [ X8 - 18 ]
Tb = 49,5, pk = 5, fks = 7, f( K(D4) ) = 11
---
D4 = 49,5 + ( 16 - 7 )/11 . 5
D4 = 49,5 + 9/11 . 5
D4 = 49,5 + 45/11
D4 = 49,5 + 4,0909..
D4 = 53,5909..
Bagian F
P65 = 65/100(40) = 13/20(40) = X26 => K( 55 - 50 ) [ X19 - 33 ]
Tb = 54,5, pk = 5, f( K(P65) ) = 15, fks = 18
---
P65 = 54,5 + ( 26 - 18 )/15 . 5
P65 = 54,5 + 8/3
P65 = 54,5 + 2,666..
P65 = 57,1666..
----
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]
Caranya juga ada dalam sini