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Bab 3 Pengukuran © 2002 Prentice-Hall, Inc. Chap 3-1 Topik  Ukuran Pemusatan  Mean, median, mode, geometric mean, midrange  Quartile  Ukuran Keragaman   Range, interquartile range, variance and standard deviation, coefficient of variation Shape  Symmetric, skewed, using box-and-whisker plots © 2002 Prentice-Hall, Inc. Chap 3-2 Pengukuran Pengukuran Central Tendency Mean Quartile Mode Median Range Variation Coefficient of Variation Variance Geometric Mean © 2002 Prentice-Hall, Inc. Standard Deviation Chap 3-3 Pengukuran Pemusatan Central Tendency Ratarata n X  Median X i 1 N  i 1 Geometric Mean X G   X1  X 2  n X i Mode  Xn  1/ n i N © 2002 Prentice-Hall, Inc. Chap 3-4 Rata-rata (Mean)  Nilai rata-rata aritmatik  Sample mean Sample Size n X  X i 1 i n  Xn Population mean Population Size N  © 2002 Prentice-Hall, Inc. X1  X 2   n X i 1 N i X1  X 2   N  XN Chap 3-5 (continued)   Ukuran pemusatan yang paling sering digunakan Dipengaruhi oleh nilai ekstrem 0 1 2 3 4 5 6 7 8 9 10 Mean = 5 © 2002 Prentice-Hall, Inc. 0 1 2 3 4 5 6 7 8 9 10 12 14 Mean = 6 Chap 3-6 Median  Tidak dipengaruhi oleh nilai ekstrem 0 1 2 3 4 5 6 7 8 9 10 Median = 5  0 1 2 3 4 5 6 7 8 9 10 12 14 Median = 5 Dalam posisi terurut , median terletak ditengah   If n or N is odd, the median is the middle number If n or N is even, the median is the average of the two middle numbers © 2002 Prentice-Hall, Inc. Chap 3-7 Modus (Mode)      Nilai yang sering muncul Tidak dipengaruhi oleh nilai ekstrem Digunakan pada data numeric atau categoric Mungkin saja tidak terdapat modus Atau ada beberapa modus 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Mode = 9 © 2002 Prentice-Hall, Inc. 0 1 2 3 4 5 6 No Mode Chap 3-8 Rata-rataGeometric  Useful in the measure of rate of change of a variable over time X G   X1  X 2    Xn  1/ n Geometric mean rate of return  Measures the status of an investment over time RG  1  R1   1  R2   © 2002 Prentice-Hall, Inc.  1  Rn   1/ n 1 Chap 3-9 Contoh An investment of $100,000 declined to $50,000 at the end of year one and rebounded to $100,000 at end of year two: X1  $100,000 X 2  $50,000 X 3  $100,000 Average rate of return: (50%)  (100%) X  25% 2 Geometric rate of return: RG  1   50%    1  100%    1/ 2   0.50    2   1/ 2 © 2002 Prentice-Hall, Inc. 1  1  1  1  0% 1/ 2 Chap 3-10