Standard Normal Distribution and the Empirical Rule

Standard Normal Distribution and the Empirical Rule

Statistics is one of an essential part of ‘various fields, and the most important of these is Research and Development. It let you deal with a great deal of data with optimum ease. Collection of data for the research purpose such as in the case of clinical trials, hospital data, surveys etc. is expected. But dealing with this vast data to compile the results become easier due to statistical formulas. It finds its massive applications in academia. Let us have a glance at standard normal distribution and the empirical formula for having clear about it.

Standard Normal Distribution:

In statistics, it is a significant part of the normal distribution as it finds its application in various natural phenomenon. For instance, multiple parameters, such as IQ scores. Measurement error, diabetes, weight, blood pressure and heights follow the normal distribution. This systematic distribution depicts itself as a probability function and indicates the distribution of values of variables. Another name for this is bell curve or Gaussian distribution.

The main reason behind being symmetrical is that all the values of data surround near the Mean. Most often it is referred to as a Bell-shaped curve and Normal curve. Plotting a graph depicts a bell shape, and hence this is the reason behind this name.

Empirical Rule for Normal Distribution:

An empirical formula calculator is an online approach which offers instant and swift outcomes with optimum accuracy. Applying statistical formulas on the data is easy when you use the online software or tool for it. You can apply the standard deviation on the data after the standard normal distribution of data. It is worthy for estimating the proportion of numbers which are away from the Mean.

Let us make this idea more transparent with the help of an example. For instance, when we process the observations and found that about 68% of these fall within SD of +/-1 from the Mean then it dep[icts to be an important part of Empirical Rule. The curve obtained is often of a bell shape and describes the % of data within limits of SD.

Online Empirical Rule Calculator:

This popular statistical rule states that whole of the data falls within three categories of SD on both sides of the Mean. Another name for the Empirical rule is 68-95-99.7 rule or three-sigma rule. Getting the results on the online empirical rule calculator demands the calculation of mean for the entire data. After the calculation of mean, the next step is the calculation of standard deviation. The successful calculation of these would let you calculate the empirical formula. Apply the formula for your data to gain the outcome. It includes;

  1. μ – σ or  μ + σ
  2. μ – 2σ or  μ + 2σ
  3. μ – 3σ or  μ + 3σ

The above formula reflects that 68%, 95%, and 99.7% falls within the category of (a), (b) and (c). Here, (a) depicts the standard deviation 1, while (b) and (c) depict standard devaition2 and standard deviation3, respectively.