Every value of variable x is converted into the corresponding z-score.Total area under the curve is equal to 1 and.A standard normal distribution has the following properties: This is when you subtract the population mean from the data score, and divide this difference by the population's standard deviation. You can standardize any normal distribution, which is done by a process known as the standard score. The shape of the bell curve is determined only by those two parameters. In strongly dispersed distributions, there's a higher likelihood for a random data point to fall far from the mean. Changes in standard deviation tightens or spreads out the distribution around the mean. You can say that an increase in the mean value shifts the entire bell curve to the right. However, it's easy to work out the latter by simply taking the square root of the variance. It may be the case that you know the variance, but not the standard deviation of your distribution. The number of standard deviations from the mean is called the z-score. Generally, 68% of values should be within 1 standard deviation from the mean, 95% - within 2 standard deviations, and 99.7% - within 3 standard deviations. It describes how widespread the numbers are. As this distribution is symmetric about the center, 50% of values are lower than the mean, and 50% of values are higher than the mean.Īnother parameter characterizing the normal distribution is the standard deviation. In a normal distribution, the mean value ( average) is also the median (the "middle" number of a sorted list of data) and the mode (the value with the highest frequency of occurrence). Many observations in nature, such as the height of people or blood pressure, follow this distribution.
Most data is close to a central value, with no bias to left or right.
Normal distribution (also known as the Gaussian) is a continuous probability distribution.