1. LATIHAN SOAL
Dari data berikut yang disajikan dalam bentuk Tabel, Histogram, Poligon Frekuensi, Ogive
positif dan Ogive negatif, Tentukan :
a). Rata-rata hitung
b). Median
c). Modus
d) Simpangan Baku
1. Tabel
Nilai
f
51-60
4
61-70
7
71-80
16
81-90
10
91-100
3
Jawab :
Nilai
x
f
U
u2
fu
fu2
Fk
51-60
55,5
4
-2
4
-8
16
4
61-70
65,5
7
-1
1
-7
7
11
71-80
75,5
16
0
0
0
0
27
81-90
85,5
10
1
1
10
10
37
91-100
95,5
3
2
4
6
12
40
1
45
JUMLAH
40
∑ fu
= ܺௗ + ቆ
ቇ.c
∑f
1
1
= 75 + ൬ ൰ . 10
40
2
2 1
= 75 +
4 4
૜
= ૠ૞
૝
Rata-rata :
‫ݔ‬
ഥ
‫ݔ‬
ഥ
x
ഥ
x
ഥ
dଵ
=L+൬
൰.c
dଵ + dଶ
1
9
= 70 + ൬
൰ . 10
2
9+ 6
1
3
= 70 + ൬ ൰ . 10
2
5
૚
= ૠ૟
૛
Modus :
M୭
M୭
M୭
M୭
1
N − ∑ fଶ
Me = L + ቌ2
ቍ.c
fଶ
Median :
1
Me = 70 +
2
1
Me = 70 +
2
4
Me = 70 +
8
20 − 11
൬
൰ . 10
16
90
൬ ൰
16
45
49
૚
൬ ൰ = 70
= ૠ૟
8
8
ૡ
Simpangan Baku :
ଶ
∑ f. uଶ
∑ f. u
ଶ
ଶ
σ = c .൝
− ቆ
ቇ ൡ
N
N
1 ଶ
45
σ = 100. ቊ − ൬ ൰ ቋ
40
40
1
40.45
−
σଶ = 100. ൜
ൠ
ଶ
40ଶ
40
ଶ
10
10ଶ
ଶ
σ = ଶ . ሺ1800 − 1ሻ =
. 1799
40
40ଶ
૚
σ = √૚ૠૢૢ
૝
ଶ

2. 2. Histogram
HISTOGRAM
f
12
12
9
8
7
6
5
4
3
2
1
6
7
5
4
3
1
41,5 48,5 55,5 62,5 69,5 76,5 83,5 90,5
Jawab :
Interval
nilai
Nilai
x
f
u
u2
fu
fu2
fk
41,5-48,5
42-48
45
4
-2
4
-8
16
4
48,5-55,5
49-55
52
6
-1
1
-6
6
10
55,5-62,5
56-62
59
12
0
0
0
0
22
62,5-69,5
63-69
66
7
1
1
7
7
29
69,5-76,5
70-76
73
5
2
4
10
20
34
76,5-83,5
77-83
80
3
3
9
9
27
37
83,5-90,5
JUMLAH
84-90
87
1
38
4
16
4
16
16
92
38
∑ fu
+ቆ
ቇ.c
∑f
16
+ ൬ ൰.7
38
8
+ ൬ ൰.7
19
56
+൬ ൰
19
18
૚ૡ
+2
= ૟૚
19
૚ૢ
Rata-rata :
‫ܺ = ݔ‬ௗ
ഥ
‫95 = ݔ‬
ഥ
‫95 = ݔ‬
ഥ
‫95 = ݔ‬
ഥ
‫95 = ݔ‬
ഥ
dଵ
=L+൬
൰.c
dଵ + dଶ
1
6
= 55 + ൬
൰.7
2
6+ 5
1
42
= 55 + ൬ ൰
2
11
11
84
= 55
+൬ ൰
22
22
95
ૠ
= 55
= ૞ૢ
22
૛૛
Modus :
M୭
M୭
M୭
M୭
M୭
1
N − ∑ fଶ
Me = L + ቌ2
ቍ.c
fଶ
Median :
1
19 − 10
Me = 55 + ൬
൰.7
2
12
63
6
Me = 55 + ൬ ൰
12
12
69
૜
Me = 55
= ૟૙
12
૝
Simpangan Baku :
ଶ
∑ f. uଶ
∑ f. u
σଶ = c ଶ . ൝
− ቆ
ቇ ൡ
N
N
16 ଶ
92
− ൬ ൰ ቋ
38
38
38.92 256
σଶ = 49. ൜
−
ൠ
38ଶ
38ଶ
ଶ
7
σଶ = ଶ . ሺ3496 − 256ሻ
38
ૠ
σ=
√૜૛૝૙
૜ૡ
σଶ = 49. ቊ

3. 3. Poligon Frekuensi
POLYGON FREKUENSI
f
10
8
7
6
5
4
3
2
1
10
7
6
6
5
4
2
45
52
59
66
73
80
87
Jawab :
Nilai
x
f
u
42-48
45
4
-2
4
49-55
52
6
-1
56-62
59
10
63-69
66
70-76
77-83
fu2
fk
-8
16
4
1
-6
6
10
0
0
0
0
20
5
1
1
5
5
25
73
7
2
4
14
28
32
80
6
3
9
18
54
38
84-90
87
JUMLAH
2
40
4
16
8 32
31 141
40
∑ fu
= Xୢ + ቆ
ቇ.c
∑f
31
= 59 + ൬ ൰ . 7
40
217
= 59 + ൬
൰
40
17
= 59 + 5
40
૚ૠ
= ૟૝
૝૙
Rata-rata :
x
ഥ
x
ഥ
x
ഥ
x
ഥ
x
ഥ
dଵ
=L+൬
൰.c
dଵ + dଶ
1
4
= 55 + ൬
൰.7
2
4+ 5
1
28
= 55 + ൬ ൰
2
9
9
2
= 55
+3
18
18
૚૚
= ૞ૡ
૚ૡ
Modus :
M୭
M୭
M୭
M୭
M୭
u2
nilai
fu
1
N − ∑ fଶ
Me = L + ቌ2
ቍ.c
fଶ
Median :
1
Me = 55 +
2
1
Me = 55 +
2
૚
Me = ૟૛
૛
20 − 10
൬
൰.7
10
10
൬ ൰.7
10
Simpangan Baku :
ଶ
∑ f. uଶ
∑ f. u
ଶ
ଶ
σ = c .൝
− ቆ
ቇ ൡ
N
N
31 ଶ
141
− ൬ ൰ ቋ
40
40
40.141 961
−
σଶ = 49. ൜
ൠ
40ଶ
40ଶ
7ଶ
σଶ = ଶ . ሺ5640 − 961ሻ
40
ૠ
σ=
√૝૟ૠૢ
૝૙
σଶ = 49. ቊ

4. 4. Ogive positif
KURVA OGIVE POSITIF
fk (kurang dari)
40
38
33
25
22
14
7
nilai
31,5 38,5 45,5 52,5 59,5 66,5 73,5 80,5
Jawab :
Interval
u
u2
fu
fu2
7
-4
16
-28
112
-2
4
-14
28
42
7
-3
9
-21
63
-1
1
-7
7
46-52
49
8
-2
4
-16
32
0
0
0
0
22
53-59
56
3
-1
1
-3
3
1
1
3
3
59,5-66,5
25
60-66
63
8
0
0
0
0
2
4
16
32
66,5-73,5
33
67-73
70
5
73,5-80,5
80,5-87,5
38
74-80
40
81-87
JUMLAH
77
2
1
2
1
4
5
4
5
8
3
4
9
16
15
8
45
32
-59
233
21
147
fk <
Nilai
x
31,5-38,5
0
32-38
35
38,5-45,5
7
39-45
45,5-52,5
14
52,5-59,5
f
40
Rata-rata 1 (dengan Xd = 63)
∑ fu
x = Xୢ + ቆ
ഥ
ቇ.c
∑f
−59
൰.7
‫ + 36 = ݔ‬൬
ഥ
40
−413
‫ + 36 = ݔ‬൬
ഥ
൰
40
13
‫01 − 36 = ݔ‬
ഥ
40
૛ૠ
‫ = ݔ‬૞૛
ഥ
૝૙
1
N − ∑ fଶ
Me = L + ቌ2
ቍ.c
fଶ
Median :
1
Me = 45 +
2
1
Me = 45 +
2
1
Me = 45 +
2
1
Me = 45 +
2
20 − 14
൬
൰.7
8
6
൬ ൰.7
8
42
൬ ൰
8
1
૜
5 = ૞૙
4
૝
u2
u
fu2
fu
Rata-rata 2 (dengan Xd = 49)
∑ fu
x = Xୢ + ቆ
ഥ
ቇ.c
∑f
21
‫ + 94 = ݔ‬൬ ൰ . 7
ഥ
40
147
൰
‫ + 94 = ݔ‬൬
ഥ
40
27
‫3 + 94 = ݔ‬
ഥ
40
૛ૠ
‫ = ݔ‬૞૛
ഥ
૝૙

5. Modus 1 (dengan Xd = 63)
dଵ
M୭ = L + ൬
൰.c
dଵ + dଶ
1
5
M୭ = 59 + ൬
൰.7
2
5+ 3
1
35
M୭ = 59 + ൬ ൰
2
8
4
3
M୭ = 59 + 4
8
8
ૠ
M୭ = ૟૜
ૡ
Modus 2 (dengan Xd = 49)
dଵ
M୭ = L + ൬
൰.c
dଵ + dଶ
1
1
M୭ = 45 + ൬
൰.7
2
1+5
1
7
M୭ = 45 + ൬ ൰
2
6
7
2
M୭ = 45
+1
14
14
ૢ
M୭ = ૝૟
૚૝
Simpangan Baku 1 (dengan Xd = 63)
ଶ
∑ f. uଶ
∑ f. u
σଶ = c ଶ . ൝
− ቆ
ቇ ൡ
N
N
Simpangan Baku 2 (dengan Xd = 49)
ଶ
∑ f. uଶ
∑ f. u
σଶ = c ଶ . ൝
− ቆ
ቇ ൡ
N
N
−59 ଶ
233
− ൬
൰ ቋ
σ = 49. ቊ
40
40
40.233 3481
−
σଶ = 49. ൜
ൠ
40ଶ
40ଶ
ଶ
7
σଶ = ଶ . ሺ9320 − 3481ሻ
40
ૠ
σ=
√૞ૡ૜ૢ
૝૙
ଶ
21 ଶ
147
σ = 49. ቊ
− ൬ ൰ ቋ
40
40
40.147 441
σଶ = 49. ൜
−
ൠ
40ଶ
40ଶ
ଶ
7
σଶ = ଶ . ሺ5880 − 441ሻ
40
ૠ
σ=
√૞૝૜ૢ
૝૙
ଶ