Determine whether the data will allow you to draw a normally distributed probability graph. Set up a frequency table, in which the first column represents the observation type; the second column, the frequency of each observation type; and the third column, the relative frequency for each observation type. To determine the third column, divide the frequency of the observation type (the values in the second column) by the total observations (the sum of all values in the second column). For example, if the observation type is suit for a deck of cards, put hearts, spades, diamonds and clubs in the first column and 13, 13, 13 and 13 in the second column. Write the relative frequency of hearts, 1/4, in the third column.
Draw a frequency graph using the data from the frequency table. Place the relative frequency on the y-axis, and place the type of observation on the x-axis. For each type of observation that describes the variable, draw a vertical bar that extends from the x-axis. For example, if your variable is the height of people in a group, you might make each bar represent a 5-inch increment in height.
Draw a vertical line down the center of the data on the frequency graph. If the data can be split into two mirror-image shapes, the data are symmetric. If you have symmetric data, use the standard deviation to describe the spread, and the mean to describe the center.
Look at the shape of the data above the x-axis. If the data has only one peak extending from the x-axis, it is unimodal.
Give the graph a title and label the x-axis with two parallel sets of numbers. Use the first line to represent the number of standard deviations, numbering it left to right, typically from -5 to +5. Use the second line to represent the values in the data corresponding to the number of standard deviations.
Draw a peak at 0 standard deviations. Above +1 and -1 standard deviations draw a point halfway between the peak and the x-axis.
Draw a smooth line from the peak at 0 standard deviations to nearly but not touching the graph at +2 and -2 standard deviations. Draw smooth, nearly horizontal lines close to but not touching the x-axis between +2 standard deviations and +5 standard deviations, and between -2 standard deviations and -5 standard deviations.