# PSYC 241 Lecture Notes - Lecture 4: Variance, Squared Deviations From The Mean, Statistical Inference

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Lesson 4: Variability

● Variability

○ A measure of how spread out the scores are in distribution

○ Accompanies central tendency as basic descriptive statistic

● Central Tendency and Variability

○ Central tendency = central point of distribution

○ Variability = how scores are scattered around central point

○ Central tendency and variability are the two primary values used to describe a

distribution of scores

● Variability

○ Variability

■ A descriptive measure

■ An important component of most inferential statistics

○ As a descriptive statistic

■ Measures degree of which scores are spread out or clustered together

○ For inferential statistics,

■ Provides a measure of how accurately any individual score or sample represents

entire population

○ When population variability is small, all of scores are clustered close together

■ Any individual score or sample will provide a good representation of the entire

set

○ When variability is large and scores are widely spread, one or two extreme scores can

give distorted picture of general population

● The Range

○ Total distance covered by distribution

○ From highest score to lowest score

■ Upper and lower real limits

● The Standard Deviation

○ Standard distance between a score and the mean

○ Preferable to range, because range is based on most extreme scores

○ The calculation of standard deviation can be summarized as a four-step process:

■ 1. Compute the deviation (distance from the mean) for each score

■ Column of deviation scores

■ Deviation (distance) from the mean for each raw score

■ Tell us:

■ Distance from mean for a particular score

■ Whether score is above or below the mean

■ 2. Square each deviation

■ Sum of squares Conceptual Formula

■ SS =∑X - μ2

■ Sum of squares is the summed total of the squared deviation scores

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