MEAN, MEDIAN, MODE

How to make it? FREQUENCY DISTRIBUTION TABLE A table containing array data have been grouped by class or specific categories . How to make it? 2

SEE This Data 50 32 33 73 47 45 79 40 70 38 72 61 76 65 56 54 58 85 52 74 68 42 75 43 48 44 82 62 77 67 66 46 35 57 59 55 69 25 63 64 28 23 36 3

FIRST STEPS ARE MAKE A FREQUENCY DISTRIBUTION TABLE 4

JK = 1 + 3,322 log n STEP 01 : SET NUMBER OF CLASSES (Jumlah Kelas JK) H.A. Sturges (1926) JK = number of classes n = the number of observations (data) 5

Form the data, number of classes are JK = 1 + 3,322 log 60 = 1 + 3,322 (1,778) = 1 + 5,907 = 6,907 ≈ 7 class 6

Set class interval ( Interval Kelas IK) STEP 02 : Set class interval ( Interval Kelas IK) (Xt – Xr) IK = JK Dimana : IK = class inteval Xt = highest data Xr = lower data Xt – Xr = Range 7

From the data obtained Xt = 85 and Xr = 23, then IK = ....? (Xt – Xr) IK = JK (85 – 23) IK = 7 = 8,8 ≈ 8 8

The frequency table is : Class interval Tally Frequency ( f ) 23 – 31 Ill 3 32 – 40 llll llll 8 41 – 49 IIII IIII II 10 50 – 58 IIII IIII IIII II 14 59 – 67 IIII IIII III 11 68 – 76 IIII IIII 77 – 85 IIII II 6 total 60 9

WHAT YOU NEED TO KNOW FROM THE FREQUENCY DISTRIBUTION TABLE 10

(Class Limit) lowest possible values within a class interval. Example Lower Class Limit lowest possible values within a class interval. Example In the class interval : 20-29; 30-39; 40-49 the lower class limit are 20, 30, dan 40. Upper Class Limit highest possible values within a class interval Example In the class interval 20-29; 30-39; 40-49 The highest class limit 29, 39, dan 49. 11

Class Boundaries Lower Class Boundary The real lower class boundary LCB – 0,5 Ex : Class interval 20-29; 30-39; 40-49, the LCB 19,5; 29,5; dan 39,5. Upper Class Boundary The real upper class boundary UCL+ 0,5 Ex : Class interval 20-29; 30-39; 40-49, the UCB 29,5; 39,5; dan 49,5. 12

Mid-point or class mark Mid-point ith = (LCL + UCL) : 2 Dimana : MP I = Mid point class ith (1,2,3,4,…..i) LCL = Lowe class limit UCL = Upper class limit 13

Mid point for class interval on Table 5.1 : 23 – 31 3 27 32 – 40 8 36 41 – 49 10 45 50 – 58 14 …… 59 – 67 11 68 – 76 77 – 85 6 total 60 14

Cummulative Frequency Cf : frequencies results from the merger of the class frequency with the class freqency before Cf can be calculated based on : ≤ (equal to or less than) ≥ (equal to or more than) 15

Comulative frequency for Table 5.1 : Class interval f Mid point Cf ( ≤ ) ( ≥ ) 23 – 31 3 27 32 – 40 8 36 11 41 – 49 10 45 21 50 – 58 14 54 dst 59 – 67 63 25 68 – 76 72 77 – 85 6 81 total 60 16

presented in graphical is certainly interesting 17

Polygon:…use frequency and mid point 20 15 10 5 Mid point 27 36 45 54 63 72 81 18

Histogram:…use freq and lower class boundary frequency HISTOGRAM 20 15 10 5 LCB 22,5 31,5 40,5 49,5 58,5 67,5 76,5 85,5 19

Ogive:…use cummulaive freq dan lower class boundary Cf 60 Less than OGIVE 20 more than 5 Lower class boundary 22,5 31,5 40,5 49,5 58,5 67,5 76,5 20

Exercise : Make a complete frequency distribution tables and graphs of polygons, histograms, and the ogive of the data distribution follows 86 63 44 75 74 54 84 78 58 77 61 72 52 73 64 66 56 68 76 71 87 48 83 94 96

Apa yang dimaksud UKURAN PEMUSATAN ? Ukuran nilai pusat yaitu nilai yang mewakili suatu deretan/ rangkaian/gugusan data Ukuran Pemusatan mencakup : MEAN, MEDIAN,dan MODUS 22

Data Tidak Dikelompokkan MEAN, MEDIAN, MODUS Data Tidak Dikelompokkan

MEAN (Me) ---- rata-rata hitung Diperoleh dengan menjumlahkan seluruh nilai data (x1+ x2 +…+ xi) dibagi dengan banyaknya data (n). Rata-rata hitung yang diambil dari data sampel dilambangkan dengan x bar = x x = Σ xi n i=1 x x1+x2+x3…xi n = atau

Contoh 6.1 : mean data tidak dikelompokkan Mata Kuliah Nilai P.Statistik 10 Azas-azas Manajemen 8 Perilaku Organisasi 7 MSDM PPSDM 9 Matematika 6 Olah Raga Jumlah 54 Mean (54 : 7) = 7,7

MEDIAN (Md) Nilai yang ada di tengah-tengah rangkaian data, setelah diurutkan dari data dengan nilai terkecil sampai terbesar. Letak Md data tidak dikelompokkan dicari dengan : LMd = (n + 1) : 2 n adalah banyaknya data

Nilai setelah diurutkan Contoh 6.2 : Median data tidak dikelompokkan LMd = (7 + 1) : 2 = 4 (median terletak pada urutan data ke 4) Nilai Nilai setelah diurutkan Urutan 10 6 Pertama 8 7 Kedua Ketiga Keempat 9 .. n = 7 Nilai Md

Bagaimana menentukan Md jika banyaknya data adalah genap ? Nilai Nilai setelah diurutkan 10 6 8 7 9 LMd = (8 + 1) : 2 = 4,5 Median terletak pada data urutan ke 4,5 atau antara urutan ke 4 dan 5. Berapa Nilainya ? Md = (7 + 8) : 2 = 7,5