stat ch.13

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