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8 Cards in this Set

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Steps for Modeling Data
1. Start with a histogram
2.Look for outliers and overall pattern
3.Give numerical summaries for center and spread
4. If pattern is regular then model with a smooth curve called a density curve.
Density Curve
A mathematical function that describes the overall pattern of the data and the underlying population.
Notation of density curves(population) vs. histograms(samples)
CENTER:
HISTOGRAM: x bar is the mean
s=std.dev & s2 is variance
DENSITY CURVE:
mu=mean,sigma=std.dev, sigma square=variance
Why model with density curves
1.Easy to investigate population properties
2.Can estimate probabilities of various outcomes
3.
Properties of density curves
1.Always on or above the x axis
2.Total area under curve=1 (or 100%)
3.Area under curve between two values:proportion of population in that interval
Imp Point
1.The MEAN is the balance point of the density curve
2.The MEDIAN divides the area of the density curve by half
Mean vs Median
For sumetric distributions:
Balance point=point dividing in half thus Mean=Median
Mean v Median for skewed distributions
Mean is always further to the skewed area i.e.:
RIGHT SKEWED:
Mean is right of median
LEFT SKEWED:
Mean is left of median
Mean and Median are not equal when we have a skewed distribution.