Transcript NORMAL DISTRIBUTIONS

NORMAL DISTRIBUTIONS
When the graph a your data looks like this shape then the shape
Or distribution of your data is consider mound or bell shaped.
(often call a normal distribution)
The distribution for this data is skewed right
Notice to make the black graph look like the blue graph
You have to push left side of the graph to the right and
Pull the right side to the right.
So we call this SKEWED RIGHT
The distribution for this data is skewed left
Median
Mean
Notice to make the black graph look like the blue graph
You have to pull left side of the graph to the left and
push the right side to the left.
So we call this SKEWED LEFT
The median divides the region into to equal areas.
The yellow area = the pink area
THE MEAN IS THE BALANCE POINT OF THE DENSITY CURVE
THE MEDIAN IS THE POINT THAT DIVIDES
THE CURVE INTO EQUAL AREAS
THE MEAN IS THE BALANCE POINT
OF THE DENSITY CURVE
IF THE CURVE IS SYMMETRIC THEY
BOTH LIE AT THE CENTER OF THE
CURVE
DESCRIBE WHERE THE MEAN AND MEDIAN ARE IN EACH
OF THESE CURVES ABOVE.
CURVES THAT ARE: SYMMETRIC
SINGLE-PEAKED
BELL-SHAPED
ARE CALLED NORMAL CURVES
THEY DESCRIBE NORMAL DISTRIBUTIONS
Empirical Rule
We use the empirical rule to describe data that
are Bell Shaped
Empirical Rule
Empirical Rule
Empirical Rule
Empirical Rule
IN A NORMAL DISTRIBUTION: 68-95-99.7 RULE
μ
IS THE MEAN OF THE DATA AND
68%
σ
THE STANDARD DEVIATION
OF THE DATA FALLS WITHIN σ OF THE MEAN
95%
OF THE DATA FALLS WITHIN 2 σ OF THE MEAN
99.7% OF THE DATA FALLS WITHIN 3 σ OF THE MEAN
END
DENSITY CURVERS are use to describe the
shape of data.
THE CURVE DESCRIBES THE OVERALL PATTERN OF A
DISTRIBUTION
ALWAYS ABOVE HORIZONTAL AXIS
AREA UNDER CURVER IS EXACTLY 1