Normal Distribution
Normal Distribution
Normal distribution is a statistics, which have been widely applied of all mathematical concepts, among large number of statisticians. Abraham de Moivre, an 18th century statistician and consultant to gamblers, noticed that as the number of events (N) increased, the distribution approached, forming a very smooth curve.
He insisted that a new discovery of a mathematical expression for this curve could lead to an easier way to find solutions to probabilities of, “60 or more heads out of 100 coin flips.” Along with this idea, Abraham de Moivre came up with a model that has a drawn curve through the midpoints on the top of each bar in a histogram of normally distributed data, which is called, “Normal Curve.”
One of the first applications of the normal distribution was used in astronomical observations, where they found errors of measurement. In the seventeenth century, Galileo concluded the outcomes, with relation to the measurement of distances from the star. He proposed that small errors are more likely to occur than large errors, random errors are symmetric to the final errors, and his observations usually gather around the true values. Galileo’s theory of the errors were discovered to be the characteristics of normal distribution and the formula for normal distribution, which was found by Adrian and Gauss, well applied with the errors. In 1778, Laplace, a mathematician and astronomer, discovered the same distribution. His “Central Limit Theorem” proved that even if the distribution is “roughly distributed”, the means of the repeated samples from the distribution is nearly normal, and the larger the size of the sample, the closer the distribution of means would be to a normal distribution. Quetelet, a statistician (astronomer, mathematician, and sociologist) was the earliest to use and apply the normal distribution to human characteristics such as weight, height, and strength.
Normal distribution is a statistics, which have been widely applied of all mathematical concepts, among large number of statisticians. Abraham de Moivre, an 18th century statistician and consultant to gamblers, noticed that as the number of events (N) increased, the distribution approached, forming a very smooth curve.
He insisted that a new discovery of a mathematical expression for this curve could lead to an easier way to find solutions to probabilities of, “60 or more heads out of 100 coin flips.” Along with this idea, Abraham de Moivre came up with a model that has a drawn curve through the midpoints on the top of each bar in a histogram of normally distributed data, which is called, “Normal Curve.”
One of the first applications of the normal distribution was used in astronomical observations, where they found errors of measurement. In the seventeenth century, Galileo concluded the outcomes, with relation to the measurement of distances from the star. He proposed that small errors are more likely to occur than large errors, random errors are symmetric to the final errors, and his observations usually gather around the true values. Galileo’s theory of the errors were discovered to be the characteristics of normal distribution and the formula for normal distribution, which was found by Adrian and Gauss, well applied with the errors. In 1778, Laplace, a mathematician and astronomer, discovered the same distribution. His “Central Limit Theorem” proved that even if the distribution is “roughly distributed”, the means of the repeated samples from the distribution is nearly normal, and the larger the size of the sample, the closer the distribution of means would be to a normal distribution. Quetelet, a statistician (astronomer, mathematician, and sociologist) was the earliest to use and apply the normal distribution to human characteristics such as weight, height, and strength.