AP Statistics Chapter 2 – Describing Location in a Distribution
2.1: Measures of Relative Standing and Density Curves
Density Curve
A density curve is a curve that
• is always on or above the horizontal axis, and
• has 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 is the proportion of all observations that fall in the range.
Example
The density curve below left is a rectangle. The area underneath the curve is 40.251.
=
i
The figure on the right represents the proportion of data between 2 and 3 (1). 0.25 0.25=i
Median and Mean of a Density Curve
• The median of a density curve is the equal-areas point, the point that divides the area
under the curve in half.
• The mean of a density curve is the balance point, at which the curve would balance if
made of solid material.
• The median and mean are the same for a symmetric density curve. They both lie at the
center of the curve. The mean of a skewed curve is pulled away from the median in the
direction of the long tail.
Normal Distributions
A normal distribution is a curve that is
• mound-shaped and symmetric
• based on a continuous variable
• adheres to the 68-95-99.7 Rule
The 68-95-99.7 Rule
In the normal distribution with mean μ and standard deviation σ:
• 68% of the observations fall within 1σ of the mean μ.
• 95% of the observations fall within 2σ of the mean μ.
• 99.7% of the observations fall within 3σ of the mean μ.
AP Statistics – Summary of Chapter 2 Page 1 of 2
