The Frequency Distribution Plots menu item gives you access to three plots designed to show you the shape of a variable's distribution. These plots are:

  THE POLYGON PLOT
  THE HISTOGRAM PLOT
  THE HOLLOWGRAM PLOT

You can use the PLOTS button at the bottom of the graph to cycle through three ways of plotting the frequency information: Histogram, Hollow Histogram and Frequency Polygon. 

All three of these plots are based on the same approach for determining the shape of a variable's distribution. The three plots differ in how that shape is drawn and shown to you.

These three plots determine the shape of a variable's distribution by breaking the range of the variable's values into equal-sized intervals called BINS. They then determine the number of observations that fall into the interval (are in the BIN) and display the shape of the distribution as folows:

  The HISTOGRAM  draws a BAR for each BIN
  The HOLLOWGRAM draws a HORIZONTAL LINE for each BIN
  The POLYGON    draws a JAGGED LINE for each BIN

For each plot there is a set if red dots. These red dots are located so that their height is proportional to the frequency in the interval. The higher the red dot, the greater the frequency in the bin. The red dots are located above the midpoint of each bin, and to the right of the frequency of the bin. You can brush your cursor over the red dots to see the frequency and midpoint of the bin.

BINWIDTH
Unfortunately, all three plots are notorious for conveying an impression of the shape of the variable's distribution that is strongly dependent on the number of bins choosen. Changing the number of bins may radically change the apparent shape of the distribution. Even more unfortunately, there is no entirely satisfactory way to solve this problem.

For this reason there are two buttons on the graph that help you control the number of bins. These are the two BINWIDTH buttons at the bottom and the NEWBINS button at the top.

The two BINWIDTH buttons can be used to dynamically change the bin widths, and, consequently, the number of bins. By putting your cursor on the button and holding your mouse button down, these buttons allow you to  watch the graph change in an animated way. Clicking on the NEWBINS button gives you a dialog box that lets you customize the bin widths and midpoints (as well as the x-axis) to get a better distribution.

We recommend that you first use the BINWIDTH buttons to get a better impression of the distribution's shape, and then the NEWBINS button to choose a "nice" bin width and midpoint. "Nice" means that the distribution adequately portrays the shape of the distribution, and the bin widths, midpoints and axis details use sensible numbers.

The CURVES button can be used to add or remove several different distribution curves, including the normal distribution and several curves called "kernel density distribution curves". The kernel density distribution curves provide several alternate ways of approximating the shape of the population distribution. If the kernel density curves roughly approximate the normal distribution curve, then the variable's distribution approximates normality.

When you click on the X button at the top of the graph you will be presented with a list of variables to display (if there are only two variables, it will switch to the other variable). Clicking on a variable will change the plot to display that variable's Frequency Polygon. When you click on the Y button at the top of the graph the y axis will switch between frequency and probability.

Finally, when you click on the DATA button at the bottom of the graph, you will create a cumulative frequency table dataobject. It contains several variables specifying frequencies and cumulative frequencies, percentages and cumulative percentages, and limits and midpoints. 
