Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Exercise - Design a data set showing a bimodal probability density function

Try to design an artificial data set containing 500 "measurements" on a single variable, which shows a bimodal probability density function. Calculate the most important measures of location and variation.

Use the  DataLab  for all the work. When ready, you should come up with the following material:

  • The mean, median, and mode of your data.
  • The standard deviation, variance, skewness and kurtosis of the data.
  • Please answer the following question: if you have a skewed distribution, what about the relative location of the mean, and the mode? If you don't know the answer right now, try to do some simulations.

Hint: Bimodal density functions can be easily achieved by filling two mutually exclusive areas of the data matrix with two sets of normally distributed random numbers with different means. Use the formula editor of DataLab for creating the random numbers. As an alternative you may use the random number generator contained in the tools section of the Teach/Me distribution.

Hint: The following DataLab script generates the required random numbers exhibiting a bimodal distribution (this script is executed automatically when you click the DataLab link above):
Resize (1,500)