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Chapter 5
Chapter 5, 6, and 7
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Simon Fraser University
Psychology
PSYC 210
Cathy Mc Farland
Winter
Description
PSYC 210
CHAPTER 5 – MEASURES OF VARIABILITY (p. 75)
Variability / Dispersion – the degree to which individual data points are distributed around the mean
Range (R) – the distance from the lowest to the highest score
 R = highest number – lowest number
 Total reliance on extreme values
Interquartile Range – the range of the middle 50% of the observations
 Discards the lower and upper 25% of the distribution
 If it discards too much data then it is not a very good estimate of the overall variability
 Trimmed Samples – samples with a percentage of the extreme scores removed
 Trimmed Statistics – statistics calculated on trimmed samples
Variance
 Mean absolute deviation (m.a.d.) – the average of the absolute values of the deviations from the
mean
 Sample Variance (s ) – sum of the squared deviations about the mean divided by N – 1
( )
o
2
 Population variance (σ ) – variance of a population; usually an estimate, rarely computed
Standard Deviation (SD, s or σ) – the square root of the variance
( )
 √
Bias – a property of a statistic whose longrange average is not equal to the parameter it estimates
Expected Value or E() – the long range average of a statistic over repeated samples
Boxplot – a graphical representation of the dispersion of a sample
Boxandwhisker plot – a graphical representation of a sample
Hinges (quartiles) – those points that cut off the bottom and top quarter of a distribution
Quartile location – the location of the quartile in an ordered series

Hspread – the range between the two hinges (also the interquartile range)
Whisker – line from the top and bottom of the box to the farthest point that is no more than 1.5 times the
Hspread from the box
***see page 91***
Winsorized Variance – the variance of a winsorized sample
Winsorized Sample – a sample in which trimmed observations are replaced with the highest and lowest
values
CHAPTER 6: THE NORMAL DISTRIBUTION
Why the normal distribution is important  Many of the dependent variables are commonly assumed to be normally distributed in the
population
 If we can assume that a variable is at least approximately normally distributed, then we can make
inferences about the values of that variable
 The theoretical distribution of the hypothetical set of sample means obtained by drawing an
infinite number of samples from a specified population can be shown to be approximately normal
under a wide variety of conditions
 Most statistical procedures have assumed that a variable is normally distributed
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