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Statistical Sciences
Statistical Sciences 2035
Terry Biggs

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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