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MB1201 Business Statistics Numerical Descriptive Measure Auditorium Session 1 Shimaditya Nuraeni Tuesday, 20 January 2015

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Where Should I Invest? I got a loan to open a convenience store in Bandung. Unfortunately, the money only sufficient to open one store. To decide where to invest I have surveyed 3 possible areas, i.e. Dago, Buah Batu and Setiabudi. In each area I took 30 samples, asking the average budget they have to go shopping in a week. The summarized data are as follow. DagoBuah BatuSetiabudi Visual comparison usually difficult Needs more objective measure about the center of the data and their dispersion (Variation)

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Numerical Descriptive Measure Arithmetic Mean Median Mode Describing Data Numerically Variance Standard Deviation Coefficient of Variation Range Interquartile Range Geometric Mean Skewness Central TendencyVariationShapeQuartiles

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Measure of Central Tendency Central Tendency Arithmetic Mean Median Mode Geometric Mean Midpoint of ranked values Most frequently observed value Not affected by extreme valuesAffected by extreme values NominalOrdinalInterval/RatioRatio Population π Sample p Population μ Sample

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Example: Arithmetic vs. Geometric Mean 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: 50% decrease 100% increase The overall two-year return is zero, since it started and ended at the same level.

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Example: Arithmetic vs. Geometric Mean Use the 1-year returns to compute the arithmetic mean and the geometric mean: Arithmetic mean rate of return: Geometric mean rate of return: Misleading result More accurate result (continued)

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Quartiles Quartiles split the ranked data into 4 segments with an equal number of values per segment 25% The first quartile, Q 1, is the value for which 25% of the observations are smaller and 75% are larger Q 2 is the same as the median (50% are smaller, 50% are larger) Only 25% of the observations are greater than the third quartile Q1Q2Q3

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Measures of Variation Same center, different variation Variation Variance Standard Deviation Coefficient of Variation RangeInterquartile Range Measures of variation give information on the spread or variability of the data values.

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Measures of Variation Standard Deviation Variance Interquartile Range = Q 3 – Q 1 Range = X largest – X smallest SamplePopulation Coefficient of variation; Relative variation

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Comparing Coefficient of Variation Stock A: – Average price last year = $50 – Standard deviation = $5 Stock B: – Average price last year = $100 – Standard deviation = $5 Both stocks have the same standard deviation, but stock B is less variable relative to its price

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Z Scores A measure of distance from the mean (for example, a Z- score of 2.0 means that a value is 2.0 standard deviations from the mean) The difference between a value and the mean, divided by the standard deviation A Z score above 3.0 or below -3.0 is considered an outlier

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Z Scores Example: If the mean is 14.0 and the standard deviation is 3.0, what is the Z score for the value 18.5? The value 18.5 is 1.5 standard deviations above the mean (A negative Z-score would mean that a value is less than the mean) (continued)

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Shape of The Distribution : Skewness Five houses on a hill by the beach House Prices: $2,000,000 500,000 300,000 100,000 100,000

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Shape of The Distribution : Skewness Mean: ($3,000,000/5) = $600,000 Median: middle value of ranked data = $300,000 Mode: most frequent value = $100,000 Describes how data are distributed House Prices: $2,000,000 500,000 300,000 100,000 100,000 Sum $3,000,000

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Reminder ! 1.QUIZ a.Week 6, 17 February 2015 Chapter 1-7 b.Week 9, 10 March 2015, OR Chapter 8-9 Week 14, 14 April 2015 Chapter 8-12

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Reminder ! 2.Group Project (Video) Make video with duration 5 minutes telling us about : How can statistics be applied in daily life, or How to explain statistical concepts in popular (fun) Video must be done in groups (DG). It must be equipped with scene titles which is containing the name of the concept that will be describe and the credits that contains the names of the group member Example :

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Reminder ! 3.Next Week Material : a.Basic Probability (including Bayes’ Theorem, Conditional Probability, etc.) b.Discrete Probability (Binomial and Poisson) Prepare yourself

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THANK YOU

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Describing Data Descriptive Statistics: Central Tendency and Variation.

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