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Chp. 4 - Variability - Coggle Diagram

- - - - Multiplying each score by a constant causes the standard deviation to be multiplied by the same constant.
  - - - As a rule of thumb, roughly 70% of the scores in a distribution are located within a distance of one standard deviation from the mean, and almost all of the scores (roughly 95%) are within two standard deviations of the mean.
  - - - the variance that exists in a set of sample data is often classified as error variance. This term is used to indicate that the sample variance represents unexplained and uncontrolled differences between scores.
- - - - IQR = Q3 - Q1
      - Typically is used when measuring central tendency with the median, especially with distributions that have extreme scores or are skewed. It often can be used when there are undetermined values and open-ended distributions as well. Like the median it can be used for data measured with an ordinal scale of measurement.
  - - - Variability describes the distribution of scores. Specifically, it tells whether the scores are clustered close together or spread out over a large distance. Usually, variability is defined in terms of distance.
        
        Variability measures how well an individual score (or group of scores) represents the entire distribution. This aspect of variability is very important for inferential statistics, in which relatively small samples are used to answer questions about populations.
        
        When using a sample to represent a population, variability provides information about how much error to expect between the sample data and the population mean.
- - - - Why? Goal of inferential statistics is to use samples to draw conclusions on populations. Samples should be representative of the population. There is a special problem for variability because samples tend to be less variable than their populations. Extreme values are less likely to be obtained when selecting a sample.
  - - - Calculate the variance.
        
        Find the square root of the variance, which is the standard deviation.
- - - - Square each deviation score.
        
        Add the squared deviations.
  - - - Population standard deviation (the square root of the population variance) = square root of (SS/N)