Transcript Chapter 2 Notes

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
1
1/2
1
2
3
4
5
6
AREA = 1
1/6
1
2
3
4
5
6
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 = 0.303
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?
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
 Normal Distribution
Points of Inflection …. ONE
Standard Deviation from the MEAN