DENSITY CURVES AND THE NORMAL DISTRIBUTION Chapter 2 DENSITY CURVES AND THE NORMAL DISTRIBUTION

Density Curve A graph that represents the relative frequency distribution for a set of data It can be used to describe the overall pattern of a distribution. Often an idealized version – “Mathematical Model” ALWAYS above or on the horizontal axis ALWAYS bounds AREA = 1 AREA bounded is used to tell the proportion of observations within a range of values.

Examples 1 AREA = 1 6 1/2 1 2 3 4 5 AREA = 1 1/6 1 2 3 4 5 6

A Mathematical Model – an idealized representation of reality FROM HISTOGRAM … TO … A DESITY CURVE TOTAL AREA OF ALL BARS = 1 A Mathematical Model – an idealized representation of reality

ACTUAL % OF SCORES LESS THAN 6 .. IS THE AREA OF THE HISTOGRAM BARS

AREA OF THE APPROXIMATED DENSITY CURVE IS NOT EXACT! AREA OF SHADED REGION = 0.293 … (i.e. 0.01 lower than the actual area)

Total Area = 1.00 Area = .12 7 8

Let’s ROLL A DISTRIBUTION P.84 # 2.5 Simulate the act of “Rolling a single die” {1, 2, 3, 4, 5, 6} Clear L1 MATH >>> PRB 5:RandInt(1, 6, 100) STO  L1 WINDOW: X [1, 7]; Y [-5, 25] YScl = 5 STAT PLOT: Histogram for L1 Repeat … Are we all the same? Skip for now …

Mean and Median MEAN: If the distribution were to be made out of solid material … the MEAN would be the balancing point. MEDAIN: The point where the area under the curve is divided into to equal halves. Same ideas from last chapter … regarding the impact of skewing. Skewed Data

The “NORMAL” Distribution

Points of Inflection …. ONE Standard Deviation from the MEAN