How to Create a Normal Distribution Chart

Written by michael keenan
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Normal distribution charts are used to analyse data from standardised tests and similar surveys. Using factors called the mean and standard deviation, distribution curves help to determine how exceptional a score really is. For example, a person's SAT or ACT score is determined by how many standard deviations away from the average score that person is. By scoring this way, it is easier to determine where a person falls across a large number sample. To create a normal distribution chart, all you need to do is to calculate the mean (or average) and the standard deviation and apply it to a standard bell curve.

Skill level:

Things you need

  • Paper
  • Pencil or pen
  • Image of a bell curve

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    Plotting the curve

  1. 1

    Determine the mean. From your data set, add the values together and divide the result by the number of data points. For example, if your data set is {10, 9, 9, 8, 6, 6}, the total is 48, and the mean is 8 (i.e., 48 divided by 6).

  2. 2

    Begin calculating the standard deviation. Start with the difference between each number in the data set and the mean. In our data set, the difference between the first data point (10) and the mean (8) is 2. Repeating this for each subsequent data point gives differences of 1, 1, 0, -2, and -2.

  3. 3

    Square the differences from Step 2 and add them (4 + 1 + 1 + 0 + 4 + 4). The total is 14. Divide this number by 1 less than the total number of data points (6). Dividing 14 by 5 gives you 2.8.

  4. 4

    Calculate the square root of the number reached in Step 3, which was 2.8. The square root is about 1.67; this is the standard deviation for our data set.

  5. 5

    Draw a horizontal line on your piece of paper. Put the mean at the centre, and make each tic to the left and right equivalent to one standard deviation. In our example, 8 is the centre of the graph, 9.67 (8 + 1.67) is one tic to the right, and 6.33 (8 - 1.67) is one tic to the left.

  6. 6

    Copy the normal distribution curve onto your graph (the curve will peak at the mean, in the centre). About 68 per cent of the area under the curve will be within one standard deviation of the mean. About 95 per cent will be within two standard deviations.

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