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
X

Mean M 
• Example?
N
• 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
Indicates how spread out the
scores are in a distribution
(are scores highly similar or not?)
• 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
Measures of Spread
The Variance
• Formula for the variance:
SS- Sum of
Squares
 (X  M)
2
SD
2

SD=Standard Deviation
(when squared = variance)
N
SS

N
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 
SD
2

 (X
 M)
2
N

SS
N
SD Computational Formula:
• Easier to use w/large data sets
• Uses sum of x scores (X) and sum of squared x
scores (X2)
• SD2 = X2 – [(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