Ch. 4 - Variability
Wednesday, September 19, 2013:06 PM
Variability
- Beyond typical value --> typical dispersion
- Intuition: spread, range, spread, "more or less"
- Problem:
○ Increase in variability =
Decrease in predictability
Decrease in homogeneity
Increase in Heterogeneity
- Goal : measure spread of scores in a distribution
- Descriptive : degree to which scores in a sample are spread out or clustered
- Inferential : how accurately any one score or sample represents the population
○ Small V = scores clustered --> any score gives a good representation of the population
○ Large V = scores widely spread --> a few extreme scores can give a distorted picture of the general
population
MeasuringVariability
- Variability can be measured by the
○ Range
○ Standard deviation & variance
- Between scores, variability measures distance
Range
- Total distance spanned by sample scores
- "rough" (approximation, unrefined)
Only reflects extremes (typical = middle) ○ Only reflects extremes (typical = middle)
○ Unstable
- Fast and easy to calculate
- Value (e.g., winter temperature)
StandardDeviation
- "Normal", "common", "typical", dispersion
○ e.g., 7 +- 2, "more or less"
- Try average distance between scores & mean
Calculate"average"distance
- Sum deviations for each score (value -- mean)
Sum of squared deviationsscore to mean?
Variance
- Sum of Squares (SS): good measure of overall variability, but dependenton the number of scores
- So, we calculate the average variability: SS/(n-1)
2
- This value is called the variance (s )
Note: N-1, not N
StandardDeviation
- Sample variance : s 2
- Population variance : σ 2
StandardDeviation:calculation StandardDeviation:calculation
StandardDeviationProperties
- Add constant to every score in a sample?
○ Standard deviation does not change
○ Visualize histogram: adding a constant moves every score, whole package just shifts
- Multiply each score by a constant?
○ Standard deviation is multiplied by the same constant
○ This multiplies the distance between scores
Usi

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