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TUGAS STATISTIKA PENDIDIKAN FISIKA “ UKURAN PUSAT,UKURAN LETAK, DAN UKURAN SIMPANGAN “
KELOMPOK IV : 1. 2. 3. 4. 5.
JEREMIA VINCENSIUS (17033020) DONA FITRI AYU (17033010) IDA FITRI (17033018) RESAWANDA (17033066) AFIFAH (17033002) Dosen Pembimbing MK : Fanny Rahmatina Rahim,S.Pd,M.Pd.
JURUSAN FISIKA FAKULTAS MATEMATIKA DAN IPA UNIVERSITAS NEGERI PADANG 2017
DATA 1
Data
Fi
FR(%)
FK
Xi
Fi.Xi
Ci
Ci.Fi
Log Xi
Fi.Log Xi
Fi/Xi
lXi–Ẋl
50-56 57-63 64-70 71-77 78-84 85-91
1 1 3 6 4 5 20
5 5 15 30 20 25
1 2 5 11 15 20
53 60 67 74 81 88 423
53 60 201 444 324 440 1522
-3 -2 -1 0 1 2 -3
-3 -2 -3 0 4 10 6
1,724 1,778 1,826 1,869 1,908 1,944 11,049
1,724 1,778 5,478 11,214 7,632 9,72 37,546
0,018 0,016 0,044 0,081 0,049 0,056 0,264
23,1 16,1 9,1 2,1 4,9 11,9 67,2
∑Fi lXi– Ẋl 23,1 16,1 27,3 12,6 19,6 59,5 158,2
(Xi-Ẋ)2
Fi(Xi-Ẋ)2
533,61 259,21 82,81 4,41 24,01 141,61 1045,66
533,61 259,21 248,43 26,46 96,04 708,05 1871,8
Rentang Kelas R
= Nilai Max – Nilai Min = 89 – 50 = 39
Banyak Kelas K
= 1 + 3,3 Log n = 1 + 3,3 Log 20 = 1+ 3,3 . 1,30 = 1 + 4,29 = 5,29 6
Panjang Kelas P
= R/K = 39 / 6 = 6,5 7
Mean Ẋ = ∑Fi.Xi N
= 1522 = 76,1 20
∑𝐹𝑖. 𝐶𝑖 Ẋ =Xo + P ( ) ∑𝐹𝑖 = 74 + 7(6) 20 = 74 + 2,1 = 76,1
Median 𝑛
Me= b+p(2
−𝐹 𝑓 20
= 70,5 + 7( 2
) − 5 ) 6
= 70,5 + 7(5/6) = 70,5 + 5,83 = 76,33
Modus Mo = b + p(
𝑑1 ) 𝑑1 + 𝑑2
3 = 70,5 + 7( ) 3+2 = 70,5 +7(3/5) = 70,5 + 4,2 = 74,7
Rata-rata Ukur Log U
= ∑(Fi.LogXi) ∑fi =37,546 20
Log U U U
= 1,8773 = 1,8773 = 101,8773 = 75,38
10Log
Rata-rata Harmonis H
= ∑Fi ∑(Fi/Xi) = 20 0,264 = 75,75
Kuartil 𝑖𝑛
Q1
−𝐹
= b + p (4
𝑓 1.20
= 63.5 + 7( = 63,5 + 7 = 70,5
4
)
−2 ) 3
𝑖𝑛
Q2
−𝐹
= b + p (4
𝑓
)
2.20
= 70,5 + 7(
4
−5 ) 6
5
= 70,5 + 7( ) 6
= 70,5 + 5,83 = 76,33 𝑖𝑛
Q3
= b + p (4
−𝐹 𝑓 3.20
= 76,5 + 7 ( = 76,5 + 7 = 83,5
4
)
− 11 ) 4
Desil 𝑖𝑛
D1
= b + p (10
−𝐹 𝑓
)
1.20
= 56,5 + 7( 10
−1 ) 1
= 56,5 + 7 = 63,5 𝑖𝑛
D2
=b+p
(10
−𝐹 𝑓
)
2.20
= 63,5 + 7( 10
−2 ) 3
= 63,5 + 4,66 = 68,16 𝑖𝑛
D3
= b + p (10
−𝐹 𝑓 3.20
= 70,5 + 7( 10 = 70,5 + 7/6 = 70,5 + 1,16 = 71,66
)
−5 ) 6
𝑖𝑛
D4
=b+p
(10
−𝐹 𝑓
)
4.20
= 70,5 + 7( 10
−5 ) 6
= 70,5 + 21/6 = 70,5 + 3,5 = 74 𝑖𝑛
D5
= b + p (10
−𝐹 𝑓 5.20
= 70,5 + 7( 10 = 70,5 + 35/6 = 70,5 + 5,83 = 76,33
)
−5 ) 6
𝑖𝑛
D6
= b + p (10
−𝐹 𝑓 6.20
= 76,5 + 7( 10
)
− 11 ) 4
= 76,5 + 7/4 = 76,5 + 1,75 = 78,25 𝑖𝑛
D7
= b + p (10
−𝐹 𝑓 7.20
= 76,5 + 7( 10 = 76,5 + 21/4 = 76,5 + 5,25 = 81,25
)
− 11 4
)
𝑖𝑛
D8
= b + p (10
−𝐹 𝑓 8.20
= 83,5 + 7( 10
)
− 15 5
)
= 83,5 + 7/5 = 83,5 + 1,4 = 84,9 𝑖𝑛
D9
= b + p (10
−𝐹 𝑓 9.20
= 83,5 + 7( 10 = 83,5 + 21/5 = 83,5 + 4,2 = 87,7
)
− 15 5
)
Presentil 𝑖𝑛
P1
= b + p (100
−𝐹 𝑓
)
1.20
−0 = 49,5 + 7( 100 ) 1 = 49,5 + 1,4 = 50,9 𝑖𝑛
P2
= b + p (100
−𝐹 𝑓
)
2.20
−0 = 49,5 + 7( 100 ) 1 = 49,5 + 2,8 = 52,3 𝑖𝑛
P3
=b+p
(100
−𝐹 𝑓
3.20
)
−0 = 49,5 + 7( 100 ) 1 = 49,5 + 4,2 = 53,7
Simpangan Baku S
=√
∑𝐹1(𝑋𝑖 − Ẋ)2 𝑛−1
1871,8 =√ 19 = √98,515 = 9,925
Simpangan Rata-rata SR = ∑F1 lXi-Ẋl ∑Fi =158,2 20 =7,91
Variansi S2 = ∑Fi (𝑋𝑖 − Ẋ)2 n-1 = 1871,8 19 = 98,515
DATA 2
Nilai
Fi
FR(%) FK
15-28 `29-42 43-56 57-70 71-84 85-96
5 7 6 8 3 1 30
16,67 23,33 20 26,67 10 3,33
5 12 18 26 29 30
Xi
Fi.Xi
Ci
Ci.Fi
Log Xi
Fi.Log Xi
21,5 35,5 49,5 63,5 77,5 91,5 339
107,5 248,5 297 508 232,5 91,5 1485
-3 -2 -1 0 1 2 -3
-15 -14 -6 0 3 2 -30
1,332 1,550 1,694 1,802 1,889 1,961 10,228
6,66 10,85 10,164 14,416 5,667 1,961 49,718
Fi/Xi lXi–Ẋl 0,232 0,197 0,121 0,125 0,038 0,010 0,723
28 14 0 14 28 42 126
∑Fi lXi–Ẋl
(Xi-Ẋ)2
Fi(Xi-Ẋ)2
140 93 0 112 84 47 476
784 196 0 196 784 1764 3724
3920 1372 0 1568 2352 1764 10976
Rentang Kelas R = Nilai Max – Nilai Min = 95-15 = 80
Banyak Kelas K = 1 + 3,3 Log n = 1 + 3,3 Log 30 = 1 + 3,3 . 1,47 = 5,851 6
Panjang Kelas P = R/K = 80/6 = 13,33 14
Mean Ẋ = ∑Fi.Xi N 30
= 1485 = 49,5
∑𝐹𝑖. 𝐶𝑖 Ẋ =Xo + P ( ) ∑𝐹𝑖 = 63,5 + 14 (−30)
30 = 63,5 -14 = 49,5
Median 𝑛
Me = b+p (2
−𝐹 𝑓
)
30
= 42,5 + 14 ( 2
− 12 ) 6
= 42,5 + 14 (3/6) = 42,5 + 7 = 49,5
Modus Mo = b + p (
𝑑1 ) 𝑑1 + 𝑑2 2
= 56,5 + 14 ( ) 2+5 = 56,5 +14 (2/7) = 56,5 + 4 = 60,5
Rata-rata Ukur Log U = ∑(Fi.LogXi) ∑fi =49,718 30 Log U = 1,657 10Log U = 1,657 U = 101,657 = 45,394
Rata-rata Harmonis H
= ∑Fi ∑(Fi/Xi) = 30 0,723 = 41,493
Kuartil 𝑖𝑛
Q1
= b + p (4
−𝐹 𝑓
)
1.30
= 28.5 + 14 (
4
2,5
−5 ) 7
= 28,5 + 14 ( 7 ) = 28,5 + 5 = 33,5
𝑖𝑛
Q2
= b + p (4
−𝐹 𝑓
)
2.30
= 42,5 + 14 (
4
− 12 ) 6
3
= 42,5 + 14 (6) = 42,5 + 7 = 49,5
𝑖𝑛
Q3
= b + p (4
−𝐹 𝑓
)
3.30
= 56,5 + 14 (
4
− 18 ) 8
4,5
=56,5 + 14( 8 ) = 56,5 + 7,875 = 64,375
Desil 𝑖𝑛
D1
= b + p (10
−𝐹 𝑓
)
1.30
= 14,5 + 14 ( 10
−0 ) 5
= 14,5 + 8,4 = 22,9 𝑖𝑛
D2
= b + p (10
−𝐹 𝑓
)
2.30
= 28,5 + 14 ( 10 = 28,5 + 2 = 30,5
−5 ) 7
𝑖𝑛
D3
= b + p (10
−𝐹 𝑓
)
3.30
= 28,5 + 14 ( 10
−5 ) 7
= 28,5 + 8 = 36,5 𝑖𝑛
D4
=b+p
(10
−𝐹 𝑓
)
4.30
= 28,5 + 14 ( 10
−5 ) 7
= 28,5 + 14 = 42,5 𝑖𝑛
D5
= b + p (10
−𝐹 𝑓
)
5.30
= 42,5 + 14 ( 10 = 42,5 + 7 = 49,5
− 12 6
)
𝑖𝑛
D6
= b + p (10
−𝐹 𝑓
)
6.30
= 42,5 + 14 ( 10 = 42,5 + 14 = 56,5
− 12 ) 6
𝑖𝑛
D7
= b + p (10
−𝐹 𝑓
)
7.30
= 56,5 + 14 ( 10
− 18 ) 8
= 56,5 + 5,25 =61,75
𝑖𝑛
D8
=b+p
(10
−𝐹 𝑓
)
8.30
= 56,5 + 14 ( 10
− 18 ) 8
= 56,5 + 10,5 = 67 𝑖𝑛
D9
= b + p (10
−𝐹 𝑓
)
9.30
= 70,5 + 14 ( 10 = 70,5 + 4,66 = 75,16
− 26 3
)
Persentil 𝑖𝑛
P1
= b + p (100
−𝐹 𝑓
)
1.30
−0 = 14,5 + 14 ( 100 ) 3 = 14,5 + 0,84 = 15,34
𝑖𝑛
P2
= b + p (100
−𝐹 𝑓 2.30
)
−0 = 14,5 + 14 ( 100 ) 5 = 14,5 + 1,68 = 16,18
𝑖𝑛
P3
= b + p (100
−𝐹 𝑓
)
3.30
−0 = 14,5 + 14 ( 100 ) 5 = 14,5 + 2,52 = 17,02
Simpangan Rata-rata Rs = ∑F1 lXi-Ẋl ∑Fi =476 30 =15,86
Simpangan Baku
S
=√
∑𝐹1(𝑋𝑖 − Ẋ)2 𝑛−1
=√
10976 29
= √378,482 = 19,454
Variansi S2 = ∑Fi (𝑋𝑖 − Ẋ)2 n-1 = 10976 29 =378,482
KELOMPOK IV : 1. 2. 3. 4. 5.
JEREMIA VINCENSIUS (17033020) DONA FITRI AYU (17033010) IDA FITRI (17033018) RESAWANDA (17033066) AFIFAH (17033002) Dosen Pembimbing MK : Fanny Rahmatina Rahim,S.Pd,M.Pd.
JURUSAN FISIKA FAKULTAS MATEMATIKA DAN IPA UNIVERSITAS NEGERI PADANG 2017
DATA 1
Data
Fi
FR(%)
FK
Xi
Fi.Xi
Ci
Ci.Fi
Log Xi
Fi.Log Xi
Fi/Xi
lXi–Ẋl
50-56 57-63 64-70 71-77 78-84 85-91
1 1 3 6 4 5 20
5 5 15 30 20 25
1 2 5 11 15 20
53 60 67 74 81 88 423
53 60 201 444 324 440 1522
-3 -2 -1 0 1 2 -3
-3 -2 -3 0 4 10 6
1,724 1,778 1,826 1,869 1,908 1,944 11,049
1,724 1,778 5,478 11,214 7,632 9,72 37,546
0,018 0,016 0,044 0,081 0,049 0,056 0,264
23,1 16,1 9,1 2,1 4,9 11,9 67,2
∑Fi lXi– Ẋl 23,1 16,1 27,3 12,6 19,6 59,5 158,2
(Xi-Ẋ)2
Fi(Xi-Ẋ)2
533,61 259,21 82,81 4,41 24,01 141,61 1045,66
533,61 259,21 248,43 26,46 96,04 708,05 1871,8
Rentang Kelas R
= Nilai Max – Nilai Min = 89 – 50 = 39
Banyak Kelas K
= 1 + 3,3 Log n = 1 + 3,3 Log 20 = 1+ 3,3 . 1,30 = 1 + 4,29 = 5,29 6
Panjang Kelas P
= R/K = 39 / 6 = 6,5 7
Mean Ẋ = ∑Fi.Xi N
= 1522 = 76,1 20
∑𝐹𝑖. 𝐶𝑖 Ẋ =Xo + P ( ) ∑𝐹𝑖 = 74 + 7(6) 20 = 74 + 2,1 = 76,1
Median 𝑛
Me= b+p(2
−𝐹 𝑓 20
= 70,5 + 7( 2
) − 5 ) 6
= 70,5 + 7(5/6) = 70,5 + 5,83 = 76,33
Modus Mo = b + p(
𝑑1 ) 𝑑1 + 𝑑2
3 = 70,5 + 7( ) 3+2 = 70,5 +7(3/5) = 70,5 + 4,2 = 74,7
Rata-rata Ukur Log U
= ∑(Fi.LogXi) ∑fi =37,546 20
Log U U U
= 1,8773 = 1,8773 = 101,8773 = 75,38
10Log
Rata-rata Harmonis H
= ∑Fi ∑(Fi/Xi) = 20 0,264 = 75,75
Kuartil 𝑖𝑛
Q1
−𝐹
= b + p (4
𝑓 1.20
= 63.5 + 7( = 63,5 + 7 = 70,5
4
)
−2 ) 3
𝑖𝑛
Q2
−𝐹
= b + p (4
𝑓
)
2.20
= 70,5 + 7(
4
−5 ) 6
5
= 70,5 + 7( ) 6
= 70,5 + 5,83 = 76,33 𝑖𝑛
Q3
= b + p (4
−𝐹 𝑓 3.20
= 76,5 + 7 ( = 76,5 + 7 = 83,5
4
)
− 11 ) 4
Desil 𝑖𝑛
D1
= b + p (10
−𝐹 𝑓
)
1.20
= 56,5 + 7( 10
−1 ) 1
= 56,5 + 7 = 63,5 𝑖𝑛
D2
=b+p
(10
−𝐹 𝑓
)
2.20
= 63,5 + 7( 10
−2 ) 3
= 63,5 + 4,66 = 68,16 𝑖𝑛
D3
= b + p (10
−𝐹 𝑓 3.20
= 70,5 + 7( 10 = 70,5 + 7/6 = 70,5 + 1,16 = 71,66
)
−5 ) 6
𝑖𝑛
D4
=b+p
(10
−𝐹 𝑓
)
4.20
= 70,5 + 7( 10
−5 ) 6
= 70,5 + 21/6 = 70,5 + 3,5 = 74 𝑖𝑛
D5
= b + p (10
−𝐹 𝑓 5.20
= 70,5 + 7( 10 = 70,5 + 35/6 = 70,5 + 5,83 = 76,33
)
−5 ) 6
𝑖𝑛
D6
= b + p (10
−𝐹 𝑓 6.20
= 76,5 + 7( 10
)
− 11 ) 4
= 76,5 + 7/4 = 76,5 + 1,75 = 78,25 𝑖𝑛
D7
= b + p (10
−𝐹 𝑓 7.20
= 76,5 + 7( 10 = 76,5 + 21/4 = 76,5 + 5,25 = 81,25
)
− 11 4
)
𝑖𝑛
D8
= b + p (10
−𝐹 𝑓 8.20
= 83,5 + 7( 10
)
− 15 5
)
= 83,5 + 7/5 = 83,5 + 1,4 = 84,9 𝑖𝑛
D9
= b + p (10
−𝐹 𝑓 9.20
= 83,5 + 7( 10 = 83,5 + 21/5 = 83,5 + 4,2 = 87,7
)
− 15 5
)
Presentil 𝑖𝑛
P1
= b + p (100
−𝐹 𝑓
)
1.20
−0 = 49,5 + 7( 100 ) 1 = 49,5 + 1,4 = 50,9 𝑖𝑛
P2
= b + p (100
−𝐹 𝑓
)
2.20
−0 = 49,5 + 7( 100 ) 1 = 49,5 + 2,8 = 52,3 𝑖𝑛
P3
=b+p
(100
−𝐹 𝑓
3.20
)
−0 = 49,5 + 7( 100 ) 1 = 49,5 + 4,2 = 53,7
Simpangan Baku S
=√
∑𝐹1(𝑋𝑖 − Ẋ)2 𝑛−1
1871,8 =√ 19 = √98,515 = 9,925
Simpangan Rata-rata SR = ∑F1 lXi-Ẋl ∑Fi =158,2 20 =7,91
Variansi S2 = ∑Fi (𝑋𝑖 − Ẋ)2 n-1 = 1871,8 19 = 98,515
DATA 2
Nilai
Fi
FR(%) FK
15-28 `29-42 43-56 57-70 71-84 85-96
5 7 6 8 3 1 30
16,67 23,33 20 26,67 10 3,33
5 12 18 26 29 30
Xi
Fi.Xi
Ci
Ci.Fi
Log Xi
Fi.Log Xi
21,5 35,5 49,5 63,5 77,5 91,5 339
107,5 248,5 297 508 232,5 91,5 1485
-3 -2 -1 0 1 2 -3
-15 -14 -6 0 3 2 -30
1,332 1,550 1,694 1,802 1,889 1,961 10,228
6,66 10,85 10,164 14,416 5,667 1,961 49,718
Fi/Xi lXi–Ẋl 0,232 0,197 0,121 0,125 0,038 0,010 0,723
28 14 0 14 28 42 126
∑Fi lXi–Ẋl
(Xi-Ẋ)2
Fi(Xi-Ẋ)2
140 93 0 112 84 47 476
784 196 0 196 784 1764 3724
3920 1372 0 1568 2352 1764 10976
Rentang Kelas R = Nilai Max – Nilai Min = 95-15 = 80
Banyak Kelas K = 1 + 3,3 Log n = 1 + 3,3 Log 30 = 1 + 3,3 . 1,47 = 5,851 6
Panjang Kelas P = R/K = 80/6 = 13,33 14
Mean Ẋ = ∑Fi.Xi N 30
= 1485 = 49,5
∑𝐹𝑖. 𝐶𝑖 Ẋ =Xo + P ( ) ∑𝐹𝑖 = 63,5 + 14 (−30)
30 = 63,5 -14 = 49,5
Median 𝑛
Me = b+p (2
−𝐹 𝑓
)
30
= 42,5 + 14 ( 2
− 12 ) 6
= 42,5 + 14 (3/6) = 42,5 + 7 = 49,5
Modus Mo = b + p (
𝑑1 ) 𝑑1 + 𝑑2 2
= 56,5 + 14 ( ) 2+5 = 56,5 +14 (2/7) = 56,5 + 4 = 60,5
Rata-rata Ukur Log U = ∑(Fi.LogXi) ∑fi =49,718 30 Log U = 1,657 10Log U = 1,657 U = 101,657 = 45,394
Rata-rata Harmonis H
= ∑Fi ∑(Fi/Xi) = 30 0,723 = 41,493
Kuartil 𝑖𝑛
Q1
= b + p (4
−𝐹 𝑓
)
1.30
= 28.5 + 14 (
4
2,5
−5 ) 7
= 28,5 + 14 ( 7 ) = 28,5 + 5 = 33,5
𝑖𝑛
Q2
= b + p (4
−𝐹 𝑓
)
2.30
= 42,5 + 14 (
4
− 12 ) 6
3
= 42,5 + 14 (6) = 42,5 + 7 = 49,5
𝑖𝑛
Q3
= b + p (4
−𝐹 𝑓
)
3.30
= 56,5 + 14 (
4
− 18 ) 8
4,5
=56,5 + 14( 8 ) = 56,5 + 7,875 = 64,375
Desil 𝑖𝑛
D1
= b + p (10
−𝐹 𝑓
)
1.30
= 14,5 + 14 ( 10
−0 ) 5
= 14,5 + 8,4 = 22,9 𝑖𝑛
D2
= b + p (10
−𝐹 𝑓
)
2.30
= 28,5 + 14 ( 10 = 28,5 + 2 = 30,5
−5 ) 7
𝑖𝑛
D3
= b + p (10
−𝐹 𝑓
)
3.30
= 28,5 + 14 ( 10
−5 ) 7
= 28,5 + 8 = 36,5 𝑖𝑛
D4
=b+p
(10
−𝐹 𝑓
)
4.30
= 28,5 + 14 ( 10
−5 ) 7
= 28,5 + 14 = 42,5 𝑖𝑛
D5
= b + p (10
−𝐹 𝑓
)
5.30
= 42,5 + 14 ( 10 = 42,5 + 7 = 49,5
− 12 6
)
𝑖𝑛
D6
= b + p (10
−𝐹 𝑓
)
6.30
= 42,5 + 14 ( 10 = 42,5 + 14 = 56,5
− 12 ) 6
𝑖𝑛
D7
= b + p (10
−𝐹 𝑓
)
7.30
= 56,5 + 14 ( 10
− 18 ) 8
= 56,5 + 5,25 =61,75
𝑖𝑛
D8
=b+p
(10
−𝐹 𝑓
)
8.30
= 56,5 + 14 ( 10
− 18 ) 8
= 56,5 + 10,5 = 67 𝑖𝑛
D9
= b + p (10
−𝐹 𝑓
)
9.30
= 70,5 + 14 ( 10 = 70,5 + 4,66 = 75,16
− 26 3
)
Persentil 𝑖𝑛
P1
= b + p (100
−𝐹 𝑓
)
1.30
−0 = 14,5 + 14 ( 100 ) 3 = 14,5 + 0,84 = 15,34
𝑖𝑛
P2
= b + p (100
−𝐹 𝑓 2.30
)
−0 = 14,5 + 14 ( 100 ) 5 = 14,5 + 1,68 = 16,18
𝑖𝑛
P3
= b + p (100
−𝐹 𝑓
)
3.30
−0 = 14,5 + 14 ( 100 ) 5 = 14,5 + 2,52 = 17,02
Simpangan Rata-rata Rs = ∑F1 lXi-Ẋl ∑Fi =476 30 =15,86
Simpangan Baku
S
=√
∑𝐹1(𝑋𝑖 − Ẋ)2 𝑛−1
=√
10976 29
= √378,482 = 19,454
Variansi S2 = ∑Fi (𝑋𝑖 − Ẋ)2 n-1 = 10976 29 =378,482
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