Density Curve
- a curve that is superimposed on a
relative frequency histogram to outline the shape.
Median
the point that divides the area under the
curve in half.
- Equal-areas point
Mean
the point at which the curve would balance if
made out of solid material.
- Balance point
symmetric density curve
the mean and the
median are equal.
- They lie in the center of the curve.
skewed density curve
the mean is pulled away
from the median in the direction of the long tail.
normal curves
symmetric, bell-shaped curves
that have these properties
a specific normal curve is completely described by its
mean and standard deviation.
- The mean determines the center of the distribution. It is
located at the center of symmetry of the curve.
- The
normal curves are useful for
describing many variables.
standard scores
Observations expressed in standard deviations above
or below the mean of a distribution
standard score= observation- mean/ standard devaiton
cth percentile of a distribution is
the value such that c percent of the observations lie below it and the rest lie above it.
25th percentile = First Quartile
� 50th percentile = Second Quartile (Median)
� 75th percentile = Third Quartile
For normal distributions
standard scores translate
directly into percentiles.
68-95-99.7 rule Empirical Rule.
in any normal ditribution
68% of the observations fall within
one standard deviations
95 % of the obsevations fall within
two standard deviations of the mean
99.7% of the observations fall within
three standard deviations of the mean
standard score
observations expressed in standard deviations above or below the mean of distribution
standard score of any observation is
standard score= observation-mean/ standard devation
Density Curve
- a curve that is superimposed on a
relative frequency histogram to outline the shape.
Median
the point that divides the area under the
curve in half.
- Equal-areas point
Mean
the point at which the curve would balance if
made out of solid material.
- Balance point
symmetric density curve
the mean and the
median are equal.
- They lie in the center of the curve.
skewed density curve
the mean is pulled away
from the median in the direction of the long tail.
normal curves
symmetric, bell-shaped curves
that have these properties
a specific normal curve is completely described by its
mean and standard deviation.
- The mean determines the center of the distribution. It is
located at the center of symmetry of the curve.
- The
normal curves are useful for
describing many variables.
standard scores
Observations expressed in standard deviations above
or below the mean of a distribution
standard score= observation- mean/ standard devaiton
cth percentile of a distribution is
the value such that c percent of the observations lie below it and the rest lie above it.
25th percentile = First Quartile
� 50th percentile = Second Quartile (Median)
� 75th percentile = Third Quartile
For normal distributions
standard scores translate
directly into percentiles.
68-95-99.7 rule Empirical Rule.
in any normal ditribution
68% of the observations fall within
one standard deviations
95 % of the obsevations fall within
two standard deviations of the mean
99.7% of the observations fall within
three standard deviations of the mean
standard score
observations expressed in standard deviations above or below the mean of distribution
standard score of any observation is
standard score= observation-mean/ standard devation