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

2. 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.

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

4. 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

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

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

7. Total Area = 1.00
Area = .12 7 8

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 …

9. 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

14. The “NORMAL” Distribution

15. Points of Inflection …. ONE Standard Deviation from the MEAN