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BUSINESS STATISTICS KEY STATISTICAL CONCEPTS

BUSINESS STATISTICS KEY STATISTICAL CONCEPTS. PROFESOR MAF . LUIS EDUARDO RINCÓN VALERO. KEY STATISTICAL CONCEPTS. POPULATION A population is the set of all items of interest in a statistical problem . SAMPLE A sample is a set of data drawn from the population.

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BUSINESS STATISTICS KEY STATISTICAL CONCEPTS

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  1. BUSINESS STATISTICSKEY STATISTICALCONCEPTS PROFESOR MAF. LUIS EDUARDO RINCÓN VALERO

  2. KEY STATISTICALCONCEPTS POPULATION • A populationisthe set of allitems of interest in a statisticalproblem. SAMPLE • A sampleis a set of data drawnfromthepopulation.

  3. TYPES OF DATA • QUANTITATIVE (INTERVAL) • Values are real numbers. • Allcalculations are Valid. • Data may be treated as ordinal orqualitatiVe. • ORDINAL (RANKED) • Valuesmustrepresenttherankedorder of the data. • Onlycalculationsbasedonanorderingprocess are Valid. • Data may be treated as nominal butnot as quantitatiVe. • QUALITATIVE (NOMINAL) • Values are thearbitrarynumbersthatrepresentcategories. • Onlycalculationsbasedonthefrequencies of occurrence are Valid. • Data maynot be treated as ordinal orquantitatiVe.

  4. CHOOSINGTHENUMBER OF CLASSES • Sturge’s formula fornumberof classes • Approximateclasswidth

  5. HISTOGRAMS • A histogramiscreatedbydrawingrectangleswhose bases correspondtotheclassinterVals, and thearea of eachrectangleequalsthenumber of obserVations in thatclass.

  6. RELATIVEFREQUENCYHISTOGRAMS RelatiVefrequencies are usefulwhenyou are dealingwith a sample of data, becausetheyproVideinsightsintothecorrespondingrelatiVefrequenciesforthepopulationfromwhichthesamplewastaken.

  7. SHAPES OF HISTOGRAMS • SYMMETRY A histogramissaidto be symmetricif, whenwedraw a line downthe centre of thehistogram, thetwosideshaVeidenticalshape and size. images taken from internet

  8. SKEWNESS A skewnesshistogramisonethatfeatures a longtailextendingeithertotherightortotheleft. TheformeriscalledpositiVelyskewed, and thelatteriscallednegatiVelyskewed. images taken from internet

  9. NUMBER OF MODAL CLASSES/ BELL SHAPE NUMBER OF MODAL CLASSES • A unimodalhistogramisonewith a single peak. • A bimodal histogramisonewithtwopeaks, notnecessarillyequalheight. • A multimodal histogramisonewithtwoor more peaks. BELL SHAPE A specialtype of symmetryunimodalhistogramisonethatis Bell-Shaped (NORMAL DISTRIBUTION).

  10. PIE CHART /CIRCULAR DIAGRAM • Themost popular graphicalmethodforqualitatiVe data isthe pie chart. *Chart shows annualized returns for model portfolios based on index returns for each asset class. 60/40 portfolio contains 60% U.S. equity and 40% diversified bond. The “+ International Stock” portfolio adds a 21% allocation to international equity, leaving 39% in U.S. equity and 40% in bonds. The “+ Real Estate” portfolio adds 10% allocation to a REIT index, lowering the bond allocation 5% (to 35%) and lowering the equity allocation 5% (pro-rata across U.S. and international allocation). Finally, the “+TIPS” portfolio allocates 1/3 of the remaining bond allocation to a TIPS index, resulting in a final allocation of 35.75% to U.S. equity, 19.25% to international equity, 10% to real estate, 23.33% to diversified bonds, and 11.67% to TIPS. The following indexes were used to represent the asset classes: S&P 500 TR (U.S. equity), FTSE World Ex US TR (international equity), MSCI US REIT GR (real estate), BarCap US Aggregate Bond TR (diversified bond), and BarCap Government Inflation Linked TR (TIPS). Taken:* http://data.worldbank.org/indicator/IS.VEH.NVEH.P3/countries?display=default

  11. DESCRIBINGTHERELATIONSHIPBETWEENTWO VARIABLES • Thetechniqueusedto describe therelationshipbetweentwoquantitatiVe (interVal) Variables isthescatterdiagram. Todraw a scatterdiagramweneed data fortwo Variables. In applicationswhereone Variable dependstosomedegreeontheother Variable, welabelthedependent Variable Y and theother, calledtheindependent Variable, X.

  12. DESCRIBING TIME-SERIES DATA • Besidesclassifying data bytype, we can alsoclassifythemaccordingtowhethertheobserVations are measured at same time orwhethertheyrepresentmeasurements at successiVepoints in time. Theformer are calledcross-sectional data and thelatter, time series data.

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