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Class notes Chapter 4 STATS-2126 Essentials of Statistics for the Behavioral Sciences, ISBN: 9780357035580
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1 of 13 Saturday, October 10, 2020Statistics Chapter 4 Notes
4-1 Introduction to Variability
Variability: Provides a quantitative measure of the differences between scores in a distribution
and describes the degree to which the scores are spread out or clustered together.
In general, a good measure of variability serves 2 purposes
1. Variability describes the distribution of scores. Specifically, whether the scores are
clustered close together or spread out over a large distance. Usually, variability is defined in
terms of distance. It tells how much distance is expected between one score and another,
or how much distance to expect between individual scores and the mean.
2. Measures how well an individual score (or group of scores) represents the entire
distribution. Important for inferential statistics, which are relatively small samples used to
answer questions about the population. 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.
The Range
range = Xmax - Xmin
The distance covered by the scores in the distribution, from the smallest to largest score.
An alternative definition is often used when the scores are measurements of a continuous
variable.
range = URL (for Xmax) - LRL (for Xmin) URL => upper real limit
LRL => lower real limit
An alternative definition is used for discrete variables.
range = Xmax - Xmin + 1
Problem with range as a measure of variability is that it is completely determined by those 2
extreme values and ignores the other scores within the distribution.
- The range does’t consider all the scores in the distribution, therefore, it often doesn’t give an
accurate description of the variability for the entire distribution
• Range considered a crude and unreliable measure of variability.
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