Lesson # 9

Front 1

Steps for Modeling Data

Back 1

1. Start with a histogram
2.Look for outliers and overall pattern
3.Give numerical summaries for center and spread
4. If pattern is regular then model with a smooth curve called a density curve.

Front 2

Density Curve

Back 2

A mathematical function that describes the overall pattern of the data and the underlying population.

Front 3

Notation of density curves(population) vs. histograms(samples)

Back 3

CENTER:
HISTOGRAM: x bar is the mean
s=std.dev & s2 is variance
DENSITY CURVE:
mu=mean,sigma=std.dev, sigma square=variance

Front 4

Why model with density curves

Back 4

1.Easy to investigate population properties
2.Can estimate probabilities of various outcomes
3.

Front 5

Properties of density curves

Back 5

1.Always on or above the x axis
2.Total area under curve=1 (or 100%)
3.Area under curve between two values:proportion of population in that interval

Front 6

Imp Point

Back 6

1.The MEAN is the balance point of the density curve
2.The MEDIAN divides the area of the density curve by half

Front 7

Mean vs Median

Back 7

For sumetric distributions:
Balance point=point dividing in half thus Mean=Median

Front 8

Mean v Median for skewed distributions

Back 8

Mean is always further to the skewed area i.e.:
RIGHT SKEWED:
Mean is right of median
LEFT SKEWED:
Mean is left of median
Mean and Median are not equal when we have a skewed distribution.