Gaussian Information and Courses from MediaLab, Inc.
These are the MediaLab courses that cover Gaussian and links to relevant pages within the course.
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| As defined by a Gaussian distribution curve, what percentage of values would be expected to fall within two standard deviations of the mean: | View Page |
| Which of the following statements best describes the mean and median as they relate to a normal "gaussian" distribution curve: | View Page |
| Introduction to the Normal Distribution Many of the data sets you will study will follow a similar distribution, with a peak around a certain value, and a few data points that lie outside the central cluster. This curve is called the normal distribution, the bell curve or the Gaussian distribution. A typical normal distribution and its formula are shown below: In this example, μ = 0 and σ = 1. As you can see, the population mean μ and population standard deviation σ appear explicitly in the formula for the normal curve. The normal curve appears in many areas of science, due to a mathematical result called the Central Limit Theorem. This theorem states that when many distributions are added together, the sum will look like a normal distribution, no matter what the original distributions were. So if the quantity you are measuring is the result of many factors, as most biological processes are, that quantity will often be normally distributed. | View Page |
| Calculating Acceptable Ranges Many physical and biological processes are well-modeled by a distribution having a roughly bell-like shape. This curve is called the gaussian, bell curve or normal distribution. The normal distribution has the following characteristics: 68.3% of the area lies between x̄ - 1s and x̄ + 1s 95.5% of the area lies between x̄ - 2s and x̄ + 2s 99.7% of the area lies between x̄ - 3s and x̄ + 3s For example, if a certain control gives a mean test result of .56 with standard deviation .8, then 95.5% of future tests on that control will be in the range .40 - .72, within 2 standard deviations of the mean. This sets limits on the range of values produced by the instrument on that control that will be considered acceptable and define which values may not acceptable and could indicate a problem. | View Page |
| Histograms Now we'll take the results of the glucose determinations and plot them on an X-Y axis. Ideally, we would see a graph like the one to the right. This is called a histogram--a graph or plot that lets you see how many times a certain event occurred. If we then draw a line following the data results, we would get a curve as shown in our illustration. Note that it has the general shape of a bell. This is known as the Gaussian curve or more popularly as a bell-shaped curve. | View Page |
| Standard Deviation In the illustration, you'll note that the curve is divided into eight equal sections. Each of these sections is one standard deviation or SD. In the middle of these eight sections is a line that represents the mean. The illustrated Gaussian curve shows a normal distribution, which means that most of the data are close to the mean with very few of the data points being at one extreme or the other. | View Page |
| What is a Levey-Jennings Chart? The Levey-Jennings chart usually has the days of the month plotted on the X-axis and the control observations plotted on the Y-axis. At the left is the Gaussian or "bell-shaped" curve turned on its side to show the correlation of the curve to the chart (i.e. fewer data points should appear on the upper and lower extremities of the chart, since the "bell" is thinner farther from the mean). By observing the data plotted in the L-J chart, we can determine if test results are in control and accurate, or if test results are not in control and consequently unacceptable. Use of the Westgard, Cumulative Summation Rules and the Youden plots will help establish an effective error-detecting scheme.
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