AP Statistics Review

A density curve is a curve that

• is always on or above the horizontal axis, and
• has an area exactly 1 underneath it

A density curve describes the overall pattern of a distribution. The area under the curve and above any range of values it eh proportion of all observations that fall in that range. 

• The mode is the peak point of the curve
• The median of a density curve is the equal-areas point
• The mean of a density curve is the balance point
• The median and the mean are always equal on a symmetric density curve

Example of a density curve: 

 A density curve is an idealized description of a distribution of data

• The mean of the density curve is denoted as and the standard deviation is denoted as
• When we take actual observations (a sample), we distinguish the mean of the distribution of these observations as x and the standard deviation as s

The area under the density curve and above any range of values is the proportion of all observations that fall in that range

The median of a density curve is the equal-areas point, the point that divides the area under the curve in half

The median and the mean are the same for a symmetric density curve. They both lie at the center of the curve