Variability
Definition:
Spread or dispersion of scores, differences among scores
•
Central tendency alone does not provide a complete description of a data set.
•
Central tendency glosses over differences; use one score to represent all
•
Variability points out those differences; describes how different scores are from one another.
•
Measures of central tendency and variability go hand in hand; they complement one another to provide a
more complete description of the group of scores.
Measures of Variability
1) Range:
Distance between the highest and lowest scores = highest score – lowest score
Example:
58, 73, 74, 76, 78, 81, 90, 96
Range = 96 – 58 = 38
2) Interquartile range
(IQR): the range of the middlemost 50% of scores; range after eliminating
the highest 25% of scores and the lowest 25% of scores; the distance between the 1
st
quartile and the 3
rd
quartile
58, 73, 74, 76, 78, 81, 90, 96
Interquartile range = 85.5 – 73.5 = 12
3) Standard deviation:
average distance of the scores from the mean
The range gives an answer to a relatively simple question about spread, “How far is it from the highest to
the lowest score?”
We could ask about spread in a different way, “On average, how far are scores from the
mean?”
We use a different measure of variability, standard deviation, to answer this.
a) Conceptual example for standard deviation:
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 Fall '08
 Chow
 Standard Deviation, 50%, 25%

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