Mencari Tabel Distribusi Frekuensi Data Jamak, Nilai Mean, Median, Modus, Quartil dan Desil dari Soal dibawah ini

 

Nama:Azman Sofi Nst

Npm:19110412

Kelas:TI-P1904

 

Quis

Mencari Tabel Distribusi Frekuensi Data Jamak, Nilai Mean, Median, Modus, Quartil dan Desil dari Soal dibawah ini ..

 

18 16 24 78 82 43 46 77 70 83 82
45 63 76 39 81 85 45 67 66 76 32
34 49 53 67 52 59 67 75 77 79 82
52 19 24 24 23 32 29 30 38 65 23
19 18 23 25 26 29 33 38 37 35 39

 

1.     Mencari Tabel Distribusi Frekuensi Data Jamak

A.    Data Jamak:

J= Xmaks – Xmin

 = 85 – 16

 = 69

 

B.     Banyak Kelas :

K= 1 + 3.3 log n

  = 1 + 3.3 (log 55)

  = 1 + 3.3 (1.74)

  = 1 + 5.7

  = 6.7

  = 7

 

C.     Interval Kelas :

I= J/K

  = 69/7

  =10

 

Maka Menghasilkan Table Distribusi Frekuensi :

 

kelas	Frekuensi
16 - 25	12
26 - 35	9
36 - 45	8
46 - 55	5
56 - 65	3
66 - 75	6
76 - 85	12

  

 

2.     Mencari Nilai Mean, Median, Modus, Quartil dan Desil

 

A.    Rata – rata (Mean)

 

       X = ∑ Xi.fi / n

  

 

No	Kelas	Xi	Fi	Fi.xi
1	16 – 25	20.5	12	246
2	26 – 35	30.5	9	274.5
3	36 - 45	40.5	8	324
4	46 – 55	50.5	5	252.5
5	56 – 65	60.5	3	181.5
6	66 – 75	70.5	6	423
7	76 - 85	80.5	12	966
	Total		∑fi = n = 55	∑fixi = 2667.5

 

X = ∑ Xi.fi /n

 

X = ∑fi.xi /n = 2667.5 / 55 = 48.5 = 49

 

B.     Nilai Tengah (Median)

 

M = L + (1/2n – F ).i / fm

 

No	Kategori  Nilai	fi	F
1	16 – 25	12	12
2	26 – 35	9	21
3	36 - 45	8	29
4	46 – 55	5	34
5	56 – 65	3	37
6	66 – 75	6	43
7	76 - 85	12	55

 

Ø  n/2 = 55/2 = 27.5   ( kelas ke 3 )

Ø  Tepi Bawah = L = BB Kelas Median – 0.5

      = 36 – 0.5 = 35.5

 

                                                I = ( BA – BB)

                                                  = (45 – 36) + 1

                                                  = 9 + 1

                                                  = 10

           

 

M = L + (1/2n – F ) / fm . i

                        = 35.5 + (1/2 . 55 – 21/8) x 10

                        = 35.5 + (27.5 – 21 /8) x10

                        = 35.5 + (6.5/8).10

                        = 35.5 + (0.8 x 10)

                        = 35.5 + 8

                        = 43.5

C.     Nilai Paling Sering Muncul (Modus)

 

Mo = L + i (b1 / b1 + b2)

 

No	Kategori  Nilai	fi
1	16 – 25	12
2	26 – 35	9
3	36 - 45	8
4	46 – 55	5
5	56 – 65	3
6	66 – 75	6
7	76 - 85	12

 

 

Tepi Bawah L = BB Kelas Modus  - 0.5

                     = 76 – 0.5 = 75.5

 

Interval      I =  (BA – BB ) + 1

                  = (85 – 76 ) +1

                  = 10

 

b1 = fi (modus) – fi (modus – 1)

      = 12 – 6 = 6

 

b2 = fi (modus) – fi (modus + 1)

      = 12 – 0 = 12

 

Mo = L +i (b1 / b1+b2)

= 75.5 + 10 (6/6 + 12)

= 75.5 + 10 (6/18)

= 75.5 + 10 (0.33)

= 75.5 + 3.3

= 78.8

 

 

D.    Quartil (1.2.3)

 

No	Kategori  Nilai	fi	Fk
1	16 – 25	12	12
2	26 – 35	9	21
3	36 - 45	8	29
4	46 – 55	5	34
5	56 – 65	3	37
6	66 – 75	6	43
7	76 - 85	12	55

 

Disini saya menjelaskan penyelesaian

Mencari Q1

 

                  i.n-fk

Q1 = TB + 4 / fq . I

 

i.n / 4 = 1x55 / 4 

            = 13.75

 

i.n-fk

Q1 = TB + 4 / fq . I

      = 25.5 + 13.75 – 12 / 9 X 10

      = 25.5 +1.75 / 9 X 10

      = 25.5 + 1.94

      = 27.44

     

 

E.     Desil (1.2.3.4.5.6.7.8)

 

No	Kategori  Nilai	fi	Fk
1	16 – 25	12	12
2	26 – 35	9	21
3	36 - 45	8	29
4	46 – 55	5	34
5	56 – 65	3	37
6	66 – 75	6	43
7	76 - 85	12	55

 

Disini saya menjelaskan penyelesaian

Mencari D1

                  i.n - fk

D1 = TB + 10 / fD.1

i.n /10 = 6 x30 / 10 

            = 18

 

                      i.n - fk

D1 = TB + 10 / fD.1

      = 25.5 + (18 – 12 / 9 ) x 10

      = 25.5 + (6 / 9 ) x 10

      = 25.5 + 6.6

      = 32.1