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PENYAJIAN DATA DAN UKURAN TENDENCY CENTRAL

PENYAJIAN DATA DAN UKURAN TENDENCY CENTRAL. Abdul Rohman Kimia Farmasi UGM, Fakultas Farmasi UGM Yogyakarta. Pendahuluan. Data dapat dikomunikasikan dalam 4 metode yang berbeda Verbal Written communication Tabel Grafik. “a picture is worth a thousand words”. TABULASI DATA.

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PENYAJIAN DATA DAN UKURAN TENDENCY CENTRAL

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  1. PENYAJIAN DATA DAN UKURAN TENDENCY CENTRAL Abdul Rohman Kimia Farmasi UGM, FakultasFarmasi UGM Yogyakarta

  2. Pendahuluan • Data dapatdikomunikasikandalam 4 metode yang berbeda • Verbal • Written communication • Tabel • Grafik “a picture is worth a thousand words”

  3. TABULASI DATA • Cara paling sederhanadan yang paling kuranginformatifuntukmenyajikan data adalahmelaluirincianhasilpercobaan • Sebagaicontoh: seorangpegawaidibagianpenjaminanmutudimiintaolehakanmelakukan sampling 30 kapsultetrasiklinselamaprosesproduksidanmelaporkannyake supervisor-nya

  4. Hasilujianalisis 30 kapsul

  5. Dilakukanpemeringkatan

  6. Keterangan • Data kontinyudiatasdapatdiubahkevariabeldiskrit • Asumsikanbahwajumlah yang diharapkandarikapsultetrasiklinadalah 250 mg/kapsul; maka data dapatdiringkasdenganmemfokuskanpada: • Yang memenuhiatau yang melebihidarijumlah yang terlabel • Yang tidakmelebihijumlah yang tercantum • Yang tepatmemenuhi, diatasdandibawah yang tepatmemenuhi

  7. Pengolahan data

  8. Tabulating and Graphing Numerical Data Numerical Data Frequency Distributions Cumulative Distributions Ordered Array Ogive Histograms StemandLeaf Display Polygons Tables

  9. 1. Bar graph

  10. 2. Histogram

  11. 3. Line Chart

  12. 4. Pie Chart

  13. UKURAN CENTRAL TENDENCY

  14. Measures of Central TendencyThe Shape of Distributions • With perfectly bell shaped distributions, the mean, median, and mode are identical. • With positively skewed data, the mode is lowest, followed by the median and mean. • With negatively skewed data, the mean is lowest, followed by the median and mode.

  15. NORMAL DISTRIBUTION

  16. Distribusi log- normal Dalam distribusi ini, frekuensi (kekerapan) diplotkan terhadap konsentrasi (karakteristik yang lain)

  17. Measure of central tendency • Central tendency • A statistical measure that identifies a single score as representative for an entire distribution. (Sebuahukuranstatistik yang mengidentifikasiskortunggalsebagaiperwakilanuntukseluruhdistribusi.) • The goal of central tendency is to find the single score that is most typical or most representative of the entire group.

  18. ASPEK CENTRAL TENDENCY • Central tendency melibatkanstatistikadeskriptifuntukserangkaianpengamatanataupengukuran • Ada 2 aspekpenting yang harusdipertimbangkanyaitu: • Pusatdistribusi • Mean • Mode • Median • Bagaimanapengamatan-pengamatan/nilai-nilaipengukuranterdistribusi/tersebar • Kisaran • Varians • Simpanganbaku/standardeviasi

  19. Mode • Merupakannilaidenganfrekuensikejadiantertinggi • Misal: berapakah mode darisekelompokpengukuranberikut: 2, 6, 7, 5, 3, 8, 7, 6, 5, 3, 2, 5, 4, 6, 8, 3, 4, 4, 7, 6, 5, 1, 5

  20. MODE • Monomodal distribution • Bimodial distribution • Misalsekelompokpopulasiada yang slow metabolizersdan rapid metabolizer a. Data: 2 3 4 5 6 Karena data inimasing-masingfrekuensi (kemunculan)-nyahanya 1, makadikatakantidakmemiliki modus. b. Data: 2 3 4 4 5 6 Frekuensiterbesaradalah 2 (nilaiempatmunculdua kali). Jadimodusnyaadalah 4. Rangkaian data yang memilikisatu modus disebut Mono-modus. c. Data: 2 3 4 4 5 6 6 7 Frekuensiterbesaradalahdua (munculdua kali) yaituangka 4 dan 6. Jadi modus rangkaian data iniadalah 4 dan 6. Rangkaian data inimemiliki 2 Modus ataudisebut Bi-modus.

  21. Mono mode vsBimodial

  22. Median • The number that divides a distribution of scores exactly in half. • The median is the same as the 50th percentile. • Better than mode because only one score can be median and the median will usually be around where most scores fall. • If data are perfectly normal, the mode is the median. • The median is computed when data are ordinal scale or when they are highly skewed.

  23. Median • The median is often used as a measure of central tendency when the number of scores is relatively small, when the data have been obtained by rank-order measurement, or when a mean score is not appropriate.

  24. Cara menghitung median • There are three methods for computing the median, depending on the distribution of scores. • First, if you have an odd number of scores pick the middle score. • 1 4 6 7 12 14 18 • Median is 7 • Second, if you have an even number of scores, take the average of the middle two. • 1 4 6 7 8 12 14 16 • Median is (7+8)/2 = 7.5 • Third, if you have several scores with the same value in the middle of the distribution use the formula for percentiles (not found in your book).

  25. Mean = rata-rata • The arithmetic average, computed simply by adding together all scores and dividing by the number of scores. • It uses information from every single score. • For a population: For a Sample:

  26. MeanOther Notes • If data are perfectly normal, then the mean, median and mode are exactly the same. • I would prefer to use the mean whenever possible since it uses information from EVERY score.

  27. Fraktil • IV. Fraktil • Adalahnilai-nilai data yang membagiseperangkat data yang telahdiurutkanmenjadibeberapabagian yang sama. • Kuartil. Adalahfraktil yang membagi data menjadiempatbagian yang sama. Nilai-nilaikuartildiberisimbol Q1, Q2 (samadengan Median) dan Q3. • DesiladalahFraktil yang membagi data menjadisepuluhbagian yang sama, simbolnyaadalah D1, D2, .., D9. • PersentiladalahFraktil yang membagi data menjadiseratusbagian yang sama, simbolnyaadalah P1, P2, …, P99. (Mulyono, 1992)

  28. KAPAN KITA MEMILIH JENIS UKURAN CENTRAL TENDENCY • Choosing a measure of central tendency • the level of measurement of the variable concerned (nominal, ordinal, interval or ratio); • the shape of the frequency distribution; • what is to be done with the figure obtained. • The mean is really suitable only for ratio and interval data. For ordinal variables, where the data can be ranked but one cannot validly talk of `equal differences' between values, the median, which is based on ranking, may be used. Where it is not even possible to rank the data, as in the case of a nominal variable, the mode may be the only measure available.

  29. Pengukuranvariabilitas • Variability provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together. (Variabilitasmenyediakanukurankuantitatifdarisejauhmanaskordalamdistribusitersebaratauberkumpulbersama.) • Diukurdengan: • KisARAN (RANGE) • Varians • Standardeviasi

  30. KISARAN (RANGE) • Kisaran merupakan selisih hasil penetapan yang paling besar dengan yang paling kecil. Semakin kecil selisihnya berati hasilnya semakin tepat. • range=Xhighest– Xlowest

  31. Deviasi rata-rata (mean deviation) • Deviasi rata-rata ( ) merupakandeviasimasing-masinghasilpenetapanterhadap rata-rata, dengantidakmemperhatikantandadeviasinya (positifataunegatif).

  32. Measure of variability

  33. Standardeviasi (SD) • Standardeviasimerupakanakarjumlahkuadratdeviasimasing-masinghasilpenetapanterhadapmeandibagidenganderajatkebebasannya (degrees of freedom).

  34. varians

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