# Agenda of Week V. Dispersion & RV Objective : Understanding the descriptive statistics Understanding the random variable and probability Week 4 1 Graphs.

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Agenda of Week V. Dispersion & RV Objective : Understanding the descriptive statistics Understanding the random variable and probability Week 4 1 Graphs Descriptive Descriptive 2 Dispersion Definition Probability Normal distribution Random variable 3

Review of Week IV Objective : Understanding the graphical illustration of data Understanding the descriptive statistics Definition Types Measurement Graphs 1 Descriptive 2 Central tendency Dispersion

Dispersion o How varied are observations? Table 4.9 o Range Difference between the largest (maximum) and smallest (minimum) observations: Eq. 4.7 o Inter-quartile range: Figure 4.24 Difference between the third and first quartiles On box plot

Dispersion o Variance and Standard deviation Average of the squared discrepancies of these values from their mean: Eq. 4.8, 4.9 Characteristics: p.130 Unbiasedness: Relation between population parameter and mean of corresponding statistics Degree of freedom

Dispersion o MAD Equation (4.14) o SPSS illustration Table 4.3

Central Tendency vs. Dispersion o Bear Markets P.131 Table 4.11

Random Variable o Definition A function that assigns a numerical value to each outcome in the sample space of a random experiment o Examples Variable indicating the number of hits in at 5 bats Variable indicating the number of red balls when we draw 3 balls from a bag with 3 blue balls and 2 red balls Variable indicating the height of high school student

Random Variable o Discrete random variable R.V. can have only discrete values (such as integers and natural numbers) as its values o Continuous random variable R.V. can have continuous values or interval as its values

Probability o Definition Possibility of happening a result from an event P(X=a) = P X (a): Probability that result a happens o Properties

Probability Distribution o Role Determination of probability for each value of r.v. pdf. vs. cdf: Figure 6.5 o Expected value and Variance p.219 Example 6.3

Normal Distribution o Most broadly used distribution Characteristics: Table 7.2 pdf. and cdf.: Figure 7.7, 7.8 A continuous scale Clear central tendency Tapering tails Symmetric about the mean Example: p.261

Normal Distribution o Importance Parametrics vs. nonparametrics Starting point of all kinds of statistics analyses Normality test o Empirical rule Figure 7.20

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