# Chapters 1 & 2 Displaying Order; Central Tendency & Variability Thurs. Aug 21, 2014.

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Chapters 1 & 2 Displaying Order; Central Tendency & Variability Thurs. Aug 21, 2014

Branches of Statistic and Basic Terms  Descriptive statistics  Inferential statistics  Basic terms –  Variable  Value  Score

 Levels of Measurement -  Numeric (quantitative) variable …includes Equal-interval variables Rank-order (ordinal) variables  Nominal (categorical) variables  Frequency Tables – summarize data  Can also group into intervals

Frequency Graphs  Histograms (for continuous data) and Bar Graphs (for categorical) Frequency Polygons – Display as line graph

Shapes of Frequency Distributions  Unimodal, bimodal, and rectangular

Shapes of Frequency Distributions  Symmetrical and skewed distributions  Which direction is the tail pointing? Pos/Neg?

Shapes of Frequency Distributions  Normal and kurtotic distributions  Indicates variability of the scores – clustered or spread out?

Measures of Central Tendency Mean - Example? Mode – most frequent score – Can be bimodal, multimodal Median – middle score – Arrange from lowest to highest, find midpoint – Or use shortcut for larger datasets (p. 40 ‘Steps for finding md’) Choosing a Cent Tend measure – are there outliers? – See example on p. 41 and Table 2-1 and 2-2

Measures of Spread: Variance The average of each score’s squared difference from the mean Computing variance: 1. Subtract the mean from each score 2. Square each of these deviation scores 3. Add up the squared deviation scores 4. Divide the sum of squared deviation scores by the number of scores Indicates how spread out the scores are in a distribution (are scores highly similar or not?)

Measures of Spread The Variance Formula for the variance: SD=Standard Deviation (when squared = variance) SS- Sum of Squares

What variance tells us Conceptually, it is the average of the squared deviation scores, so… – The more spread out the distribution, the larger the variance What if variance = 0? – Very important for many stat tests – Conceptual difference in unit of variance versus standard deviation?

Measures of Spread: Standard Deviation Formula for standard deviation:

SD Computational Formula: Easier to use w/large data sets Uses sum of x scores (  X ) and sum of squared x scores (  X 2 ) SD 2 =  X 2 – [(  X) 2 / N] N Note that your book prefers the definitional formula, not this one p. 51 – some instances when we divide SS by N-1 – …but we won’t do this until Ch 7

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