Assignment #21.120, 1.122, 1.126, 1.132, 1.136, 1.142, 1.146,2.22, due September 16
2Density Curves and NormalDistributions
What we have learnedPlot the dataLook for overall pattern and deviations from thepatternCompute numerical summaries
Mathematical modelIf the pattern is sufficiently regular, approximateit with a smooth curveA curve that is always on or above the horizontalaxis and has total area underneath equal to 1 iscalled adensity curve.
Density curvesAreaunder the curve in a range of valuesindicates the proportion of values in that rangeKeep in mind that density is only anapproximation(an idealized mathematicalmodel), but it simplifies analysis and is generallyaccurate enough for practical use.
Median and mean of a density curveMedian: the point with 50% of the area on eithersideMean: the balancing point of the curve, if it werea solid mass; can be calculated by usingcalculus
Mean and standard deviation of an idealizedmodelMean and standard deviation of observed data
Density curves come in a variety of shapes, butthe family of “normal” distributions with familiarbell-shapeddensity curves is commonly used
Normal distributionsAll the normal distributions can be generatedfrom thestandardnormal distribution bychanging locations and scales (lineartransformations)The standard normal distribution has densityfunction defined byIt has mean equal to 0 and variance equal to 1.