Write the data as a stem and leaf table. Create the "stems," as the x-variable of the table. Write the "leaves" as the y-variables. The stems are usually the initial digits of the data; the leaves are the number of data points with those digits. For example, if you have a set of data with the values 13, 11, 41, 21, 49, 30, and 40, your stems are "1," "2," "3" and "4" since these are the initial digits in the data. In this case, you have 2 leaves for "1," 1 leaf for "2," one leaf for "3" and 3 leaves for "4."
Plot the stem and leaf table as a bar chart. The easiest way to do this is to turn the table on its side so that the stems fall along the horizontal axis and the leaves are vertical bars.
Calculate the mean of the data. Sum the data points and divide by the number of data points. This is your mean. For the example data given above, the mean is 29.29.
Calculate the standard deviation of the data. Subtract the mean from each data point individually. Sum the resulting numbers. Divide by the number of data points. Take the square root of this resulting number. This is your standard deviation. For the example data, the standard deviation is 14.77.
Plot the normal curve over the stem and leaf plot. Use the equation of the normal curve: f(x) = exp[-(x-m)^2/(2*s^2)]/sqrt(2*pi*s^2). In this equation, "m" is the mean that you calculated, "s" is the standard deviation that you calculated, "pi" is the number 3.14 and "sqrt" means the square root function.
Check how the normal curve and the stem and leaf plot match. If it looks like the stem and leaf plot approximately fits the normal curve, it is likely that your data set is normally distributed.