Density Curves and Normal Distributions

Density curves

models the distribution of a quantitative variable with a curve that is always on or above the horizontal axis and has area exactly 1 underneath it

Mean of density curve

a the point at which the curve would balance it made of solid material

Median of a density curve

the equal-areas points, the point that divides the area under the curve in half

Normal distribution

specified by 2 parameters: mean and standard deviation

Normal Curve

described by a symmetric, single-peaked. bell-shaped density curve

Empirical rule

Approximately 68% of the observations fall within the standard deviation of the mean, approximately 95% of the observations fall within two standard deviation of the mean, approximately 99.7% of the observations fall within three standard deviation of the mean

Standard Normal Distribution

the normal distribution with mean 0 and standard deviation 1

Normal Probability Plot

a scatterplot on the ordered pair (data value, expected z-score) for each of the individuals in a quantitative data set. That is, the x-coordinate of each point is the actual data value and the y-coordinate is the expected z-score corresponding to the percentile of that data value in a standard Normal distribution