A bell-shaped graph, or bell curve, displays the distribution of variability for a given data set. For example, the most well-known example, the IQ graph, shows that the average intelligence of humans falls around a mean score of 100 and trails off in both directions around that center score. You can generate your own bell curve graphs by calculating a standard deviation and mean for any collected set of data.

### Collect Accurate Data

Carefully gather your data of interest. For example, if you study economics, you may wish to collect the average annual income of citizens of a given state. To ensure your graph looks more bell-shaped, aim for a high population sample, such as forty or more individuals.

### Calculate Sample Average

Calculate your sample mean. The mean is an average of all of your samples. To find the mean, add up your total data set and divide by the population sample size, n.

### Determine Standard Deviation

Compute your standard deviation to find out how far each score is from the average. To do this, subtract your mean from each of your individual datum. Then square the result. Add up all of these squared results and divide that sum by n – 1, which is your sample size minus one. Lastly, take the square root of this result. The standard deviation formula reads as follows: s = sqrt[ sum( (data – mean)^2 ) / (n – 1) ].

### Plot Data

Plot your mean along the x-axis. Make increments from your mean spaced by a distance of one, two and three times your standard deviation. For example, if your mean is 100 and your standard deviation is 15, then you would have a marking for your mean at x = 100, another important marking around x = 115 and x = 75 (100 + or - 15), another around x = 130 and x = 60 (100 + or - 2(15)) and a final marking around x = 145 and x = 45 (100 + or - 3(15)).

### Draw the Graph

Sketch the bell curve. The highest point will be at your mean. The y-value of your mean does not precisely matter, but as you smoothly descend left and right to your next incremental marking, you should reduce the height by about one-third. Once you pass your third standard deviation left and right of your mean, the graph should have a height of almost zero, tracing just above the x-axis as it continues in its respective direction.

#### Things You Will Need

- Calculator
- Pencil
- Paper

#### Tip

- A graphing calculator or spreadsheet can help produce means and standard deviations faster than doing all calculations by hand.

#### References

#### Photo Credits

- bell image by Vaida from Fotolia.com