The Graph shows a normal distribution. The mean is indicated by a blue line and the standard deviation is indicated by a red line on either side of the mean. The black circles at the bottom of the red lines can be dragged with the mouse to change the standard deviation. The maximum standard deviation is 1.25. The red graphic in the upper-left corner gives the scale of the grid.
You can also set the standard deviation by typing a new value in the box marked New Standard Deviation and clicking the Set button. The current standard deviation is printed in the label just below the graph.
To draw a histogram, choose the number of trials you want from the choices in the pull-down menu and click the Create New Histogram button. You can change the bin size using the scrollbar.

## Summary/Background

The normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average") and standard deviation ("variability"), respectively. The standard normal distribution is the normal distribution with a mean of zero and a variance of one (the green curves in the plots to the right).

Carl Friedrich Gauss (1777 - 1855) became associated with this set of distributions when he analyzed astronomical data using them, and defined the equation of its probability density function. It is often called the bell curve because the graph of its probability density resembles a bell.

Carl Friedrich Gauss (1777 - 1855) became associated with this set of distributions when he analyzed astronomical data using them, and defined the equation of its probability density function. It is often called the bell curve because the graph of its probability density resembles a bell.

A
note about graphic calculatorsA graphic calculator, for example the TI-83 or similar model, can display graphs of normal curves Go to the Y= screen and enter Y1 = normalpdf(X), then go
to the WINDOW screen and set Xmin=-3, Xmax=3, Ymin=0, Ymax=0.4. Then display
the GRAPH screen. |

## Software/Applets used on this page

From a collection of Java statistics applets from the Project

Interactive, Shodor Educational Foundation site at Durham, North Carolina, USA, used with permission.

Interactive, Shodor Educational Foundation site at Durham, North Carolina, USA, used with permission.

## Glossary

### density

the ratio of the mass of an object to its volume

### equation

A statement that two mathematical expressions are equal.

### function

A rule that connects one value in one set with one and only one value in another set.

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### histogram

A statistical diagram for continuous data similar to a bar chart but where the area of each bar is proportional to the frequency.

### mean

the sum of all the members of the list divided by the number of items in the list.

### normal

A line passing through a curve at a point that is perpendicular to the tangent to the curve at that same point.

### normal distribution

A key distribution in statistics which is used to model many naturally occurring phenomena, such as heights and weights; its distribution is bell-shaped.

### standard deviation

The square root of the variance; a measure of dispersion.

### variance

The square of the standard deviation; a measure of dispersion.

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S1 | The Normal Distribution | Shape | - |

AQA A2 Maths 2017 | Statistics | The Normal Distribution | Shape of Normal Distribution | - |

AQA AS/A2 Maths 2017 | Statistics | The Normal Distribution | Shape of Normal Distribution | - |

CCEA A-Level (NI) | S1 | The Normal Distribution | Shape | - |

CIE A-Level (UK) | S1 | The Normal Distribution | Shape | - |

Edexcel A-Level (UK - Pre-2017) | S1 | The Normal Distribution | Shape | - |

Edexcel A2 Maths 2017 | Statistics | The Normal Distribution | Shape of Normal Distribution | - |

Edexcel AS/A2 Maths 2017 | Statistics | The Normal Distribution | Shape of Normal Distribution | - |

I.B. Higher Level | 5 | The Normal Distribution | Shape | - |

I.B. Standard Level | 5 | The Normal Distribution | Shape | - |

Methods (UK) | M15 | The Normal Distribution | Shape | - |

OCR A-Level (UK - Pre-2017) | S2 | The Normal Distribution | Shape | - |

OCR A2 Maths 2017 | Statistics | The Normal Distribution | Shape of Normal Distribution | - |

OCR MEI A2 Maths 2017 | Statistics | The Normal Distribution | Shape of Normal Distribution | - |

OCR-MEI A-Level (UK - Pre-2017) | S2 | The Normal Distribution | Shape | - |

Pre-U A-Level (UK) | Prob | The Normal Distribution | Shape | - |

Universal (all site questions) | N | The Normal Distribution | Shape | - |

WJEC A-Level (Wales) | S2 | The Normal Distribution | Shape | - |