Measuring The Spread (measures of
variation)
Example – table showing the distribution
of annual income for 2 nations
Nation 1 Nation 2
$5000 60% $10,000 30%
$8000 25% $11,000 20%
$10,000 10% $12,000 20%
$100,000 4% $13,000 30%
$150,000 1%
x x
1= $11,500 2= $11,500 These two nations have the same mean
income, but have vastly different
distributions of wealth
• as you can see, the mean (or median)
alone does not tell the whole story
• one distribution may have a large
variation of data, while another may
have a small spread
We need to also have a measure of the
spread of a distribution Main Measures of Spread
1. Range = highest observation − lowest observation
• not very useful; ignores bulk of the
observations
2. Standard Deviation
• this is the most commonly used
measure of spread
• it is a measure of the variation of the
data about its mean (it looks at how
far the observations are from their
average value) Formula
We first calculate what is called the
variance, s , of a set of n-observations
x1, x2, … , xn
2
s =
2
s =
The standard deviation is the square root
of the variance,
2
s = s Shortcut Formula – a bit easier to use
when doing calculations by hand
s =
Notes
1. The larger the value of s, the more

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