Identify the sample mean. The more data you acquire, the more people you interview or products you test, the more accurate your mean will be. To get the mean, add all the data points together, and divide by the number of data points. For instance, if you are trying to find the average weight of a fifth-grader, you would weigh each individual in your random sample. To find the mean, add all the weights together and divide by the number of students you weighed. This is your sample mean.
Calculate the variance by subtracting the mean from every individual sample point. Square the numbers, and add them together. Then divide the total by the number of data points in your sample. For instance, if you have a sample of 1, 2, 3, 4, 5, your mean is 3. Subtract 3 from 1, 2, 3, 4, and 5 individually. This would give you -2, -1, 0, 1 and 2. Square each number, giving you 4, 1, 0, 1 and 4 and add them together. Your total would be 10. Divide by the total amount of numbers, in this case 5. Your variance is 2. This means that the average squared variation from the mean is 2.
Identify the standard deviation. The standard deviation is the square root of the variance. Using the example above, the variance is 2, so the square root of 2 is 1.414
Calculate the standard error of the mean by dividing the standard deviation from the mean by the square root of the sample size. The standard error for the above example is .6324. As the standard error decreases, the mean becomes closer to the actual population mean.
Create a bar chart with frequency on the left going up the chart and the numbers along the bottom. For instance, if there were 30 children who weighed 45 pounds, 20 who weighed 35 pounds, and 10 who weighed 55 pounds in your fifth-grade sample, your bar would go 30 high at the point of 45 pounds on the bottom of the chart, 20 high at 35 on the bottom and 10 high at 55 on the bottom of the chart. This gives you your entire distribution. You can draw a bell-curve over each of the bars, hitting the upper corners of each bar, to illustrate the distribution more clearly.
Draw a line through your bell curve at the points of standard deviation on both sides of your mean. For instance. If your mean is 3, your standard deviations will be 1.414 plus 3 and 1.414 minus 3. The lines should intersect your bell curve near their bottom curves where they start to level off on each side. This is your sample distribution.