How to Create a Bell-Shaped Curve

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The bell-shaped curve has many different applications, specially in the field of statistics. The bell shape curve (also called the "normal" distribution) is defined by two important parameters: the mean and the standard deviation. Being able to create your bell-shaped curves will allow you to better understand the mathematics behind it, and at the same time, to get a deeper knowledge of how its parameters affect the shape of the curve. Since this is a very complex curve, a computer with a spreadsheet program is necessary to create a graph.

Things You'll Need

  • Open Office Software (See Resources)

Generating the data

  • Open the Open Office software suite. Choose the Spreadsheet option to create a blank spreadsheet.

  • Go to cell A1 and write "Mean." Go to cell A2 and enter the number zero. Go to cell B1 and write "Standard Deviation;" on cell B2 enter the number one. Go to cell C1 and write "X;" on cell C2 enter the number negative-five.

  • Go to cell D1 and write "Constant term." On cell D2, enter the following: "=1/(SQRT(2PI())$B$2)" (without the quotation marks) and press "Enter." This is the constant part of the equation.

  • Go to cell E1 and write "Z." On cell E2 enter the following: "=(C2-$A$2)/$B$2" and press "Enter." This is called the Z-score equation; it is part of the exponent of the equation.

  • Go to cell F1 write "Exponent." Go to cell F2 and type "=-0.5E2E2."

  • Go to cell G1 and write "e term". On G2 enter "=EXP(F2)."

  • Go to cell H1 and write "Y." On H2 enter "=D2*G2."

  • Place your cursor on the column D. Left-click the column and, while pressing the left button, drag it to the right to highlight columns D, E, F, and G. Release the left button and click the highlighted area with the right mouse button. A small menu will appear; choose "Hide."

Creating the Graph

  • Go to the "Insert" menu and click on "Chart." Choose the "(XY) Scatter" chart type. Choose the "Lines Only" icon (the third icon starting from the left), and check the box labeled "Smooth Lines."

  • Click on "3. Data Series" from the vertical menu located at the left of the window. If you see any items on the Data Series window, click remove until it is empty.

  • Click the "Add" button to add a new data series. On the "Data Range" field click on "name." On the field bellow, type "Bell Shape Curve."

  • On the "Data Range" field, click on "X-Values." On the field below, click on the small icon on the right of the field. This will close your window, and a smaller window will appear. Click on cell C2 and, while holding the mouse's left button, drag the selection until you reach cell C52. Let go of the mouse button and click the small icon located on the right side of the small window. This will close the small window and open your insert chart window again.

  • On the "Data Range" field click on "Y-Values." On the field below, click on the small icon on the right of the field. This will close your window, and a smaller window will appear. Click on the cell H2 and, while holding the mouse's left button, drag the selection until you reach cell H52. Let go of the mouse button and click the small icon located on the right side of the small window.

  • Click the "Finish" button. Your bell-shaped graph will appear on your spreadsheet. Use the mouse to change its size and position.

Tips & Warnings

  • You can displace your graph horizontally by changing the value of the mean (on cell A2).
  • You can make your graph wider and narrower by changing the value of the standard deviation (on cell B2).
  • Check for typing mistakes. Forgetting an equal sign or a parenthesis will prevent the formulas from working properly on your spreadsheet.

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