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Normal Error Curve

Introduction

Random fluctuations result in a distribution of results when making repetitive measurements. The distribution that results due to truely random events is called a "normal error" or Gaussian curve. It is also sometimes called a "bell-shaped curve". The mathematical expression for this random distribution is:

gaussian

Where sigma is the population standard deviation: population standard deviation
and z with µ being the population mean.

This equation is plotted below. The dark vertical lines indicate the area under the curve from -1sigma to +1sigma, and the lighter lines indicate the area under the curve for ±2sigma.

Gaussian curve


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