due on 02/22/2016 - STATISTICS- RESEARCH METHOD - GRAPHIC REQUIRED - central tendency and dispersion measures

Chapter 11: Normal Distribution; Exploratory Data Analysis

Standard Deviation and Normal Curve  Standard deviation used extensively in inferential statistics; used to estimate how close a sample

characteristic is to the corresponding population parameter  Normal distribution uses the standard deviation as a ‘ruler’  Normal Curve characteristics:  Bell-shaped and symmetric  Mode, Median and Mean are equal and located at the center of the distribution  Fixed proportion of data lie between the mean and any fixed point on the curve

Empirical Rule  ~ 68% of cases fall within 1 standard deviation of the mean  ~ 95% fall within 2 standard deviations  ~ 99.7% fall within 3 standard deviations

Standard Scores/Z-scores

 Z-scores measure the distance, in standard deviations, of an observation from the mean where z is the z-score Xi is an observation is the mean of the distribution s is the standard deviation of the distribution

Exploratory Data Analysis  Emphasizes becoming familiar with the data, rather than simply summarizing with one or two statistics

 New measures of center of spread used

o Trimmed Mean: Mean is calculated after removing outliers or a % of cases

 5% Trimmed Mean: Mean calculated after the bottom and top 5% of data are removed

o Midmean: uses only the middle 50% of data

 New data displays: Box Plot, also called Box-and-Whisker

 Minimum, Q1, Median, Q3, Maximum

 Very useful for comparing two or more data sets

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XX z i

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