Section 2.1:Density curves andthe Normal Distributionsrom chapter 1 we have a strategy forexploring data on a single quantitativevariable:lot your data: make a graph, usually ahistogram or a stemplot.ook for the overall pattern (shape, center,spread) and for any striking deviations suchas outliers.2
Here is the next step:•If the overall pattern of a large number ofobservations is very regular we candescribe it with a smooth curve.This curve is a mathematical model for thedistribution and it gives a compact pictureof the overall pattern.This is also knownas a density curve.3
A density curve is a curve that:
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The Median and Mean of a Densitycurve:•The mean of a density curve is thebalance point, at which the curve wouldbalance if made of solid material.•The median of a density curve is theequal-areas point, the point that dividesthe area under the curve in half.5
•The median and mean are the samelocation if the density curve is symmetric,and they both lie at the center of the curve.The mean of a skewed curve is pulledaway from the median in the direction ofthe long tail.6
•Since a density curve is an idealizeddescription of the distribution of data, weneed to distinguish between the mean andstandard deviation of the density curveand the mean and standard deviationcomputed from the actual observations.The new notation is the Greek letter mu forthe mean and the Greek letter sigma forstandard deviation.μσ7
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Normal distributions:•Normal curves are curves that aresymmetric, single-peaked, and bell-shaped.