Mean of a Density Curve: think of a fulcrum balancing a density curve, the line inside the curve represents the mean.

• If more weight is on the left of the curve than the right, the curve would dip on the left.
• If more weight is on the right of the curve than the left, the curve would dip on the right.

Symmetric Curve: Mean and Median: the mean and median are the same for a symmetric density curve.

Mean = Median Median

Left Skewed Curve: Mean and Median: in a left skewed distribution, the mean is on the left closer to the tail of the distribution.

• The median is located at the center of the data.

   

Right Skewed Curve: Mean and Median

• In a right skewed distribution, the mean is on the right closer to the tail of the distribution.
• The median is located at the center of the data.

This tutorial shows the density curves and their properties. Many illustrative graphs are used to show you what density curve is, their shapes, and how to identify a density curve, etc.

After this tutorial you will be able to identify a density curve, name the shape of the density curve, understand the importance of the area under the density curve and locate the mean and median of a density curve.

Specific Tutorial Features:

• We use a lot of graphs in illustrating the different density curves and their shape and how to obtain their means, step by step.
  
• The way to balance density curve and the relationship between mean and median are also demonstrated in the examples.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  
• Definition slides introduce terms as they are needed.
  
• Visual representation of concepts
  
• Animated examples—worked out step by step
  
• A concise summary is given at the conclusion of the tutorial.

• Density Curve
  
• Mean of a Density Curve
  
• Median of a Density Curve