Density Curves and the Normal Distributions
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