Manipulating Histograms

http://www.ruf.rice.edu/~lane/stat_sim/descriptive/index.html

 

Objectives:

• To explore how mean and median compare on different shaped distributions.
• To examine how the standard deviation is affected by the shape of the distribution.

 

When you open this site, you must get to the right applet. To do this:

• Scroll down the left side, and choose “internet applets.”
• Choose measures of a distribution.
• Choose mean and median.
• Click “begin.”

 

 

Instructions are on the right of the screen. The idea is that you can change the data by “painting” the histogram with the mouse. You can also add bars where there aren’t any, and change the heights of other bars (which is changing the frequency of data values.) When you make a change on the histogram, notice carefully what happens to the mean, median and the standard deviation.

 

Try these exercises:

 

1. Note the mean deviation from the mean and the mean deviation from the median are both zero. Change the data and see if this is still true.

 

2. Change the distribution so that it has a positive skew (tail is on the right). Which is bigger, the mean or the median?

 

3. Change the distribution so that it has a negative skew (tail is on the left). Which is bigger, the mean or the median?

 

4. Create a uniform distribution. What is the standard deviation? Now change the distribution so that it is normal again. How does the standard deviation compare?

 

5. Find a distribution that has the smallest standard deviation you can find (with this data and frequency range).  What can you say about that distribution? Make a sketch of this distribution.

 

6. Find a standard deviation that has as large a standard deviation as you can find (with this data and frequency range). How would you describe this distribution? Make a sketch of this distribution.