Normal Distribution Explained with Real-Life Examples

 Statistics helps us understand patterns hidden inside data. One of the most important and widely used patterns in statistics is the Normal Distribution. It appears in many areas, including education, healthcare, business, science, engineering, and computer science. Understanding the normal distribution helps us describe data, compare observations, and make useful predictions.

What is a Normal Distribution?

A normal distribution is a type of distribution that has a characteristic bell shape curve. Many data values lie near the center, whereas few data values lie farther from the center.

Take an instance where we consider the height of the students in the whole population; many of them will have heights equal to the average, whereas few of them will have either very small or very large heights. In such a scenario, when the heights are plotted on a graph, they will form a bell shape. This is an example of normally distributed data.

The mean (μ) denotes the average of the values and is the center of the distribution, whereas the standard deviation (σ) shows the spread of the observations around the mean.

The Main Features

There are certain key features that can be associated with a normal distribution.

First, a normal distribution is symmetric around its mean, which means that both sides of the distribution have identical shapes.

Second, in a completely normally distributed data set, the mean, median, and mode are equal to each other and coincide at the middle point of the curve.

Third, the majority of observations are concentrated near the mean, whereas observations farther away from the mean become increasingly rare.

To better understand how observations are dispersed from the mean, we use standard deviation. Approximately 68% of observations are found within one standard deviation from the mean, 95% – within two standard deviations, and 99.7% – within three standard deviations. This is often referred to as the 68-95-99.7 rule.

 

Example in Real Life: Exam Scores

For example, assume that the scores obtained by a big number of students in an exam are normally distributed, where their mean score is 70 marks and their standard deviation is 10 marks.

Most of them will score around 70 marks. For a student who gets 80 marks, he is one standard deviation higher than the mean, whereas for a student getting 60 marks, he is one standard deviation lower than the mean.

In this way, teachers and statisticians get a good idea of how a particular student's performance is relative to the whole population.

Example in Real Life: Height

The last example commonly used is human height. When measurements of heights of human beings in sufficient number are collected, it may be normally distributed.

Most of the humans have heights around the mean height, and very short or very tall humans are not usually found.

Normal Distribution in Computer Science

The normal distribution is also useful in Computer Science and Data Science. There are different statistical and machine learning approaches that involve assumptions regarding distributions of data.

The examples of normal distributions include data analysis when studying measurement errors, experiment outcomes, model residuals, etc. The knowledge of the distribution of data allows data scientists to choose a proper statistical method to analyze their data.

An interesting concept associated with normal distribution is z-score that shows us how far away from the mean a particular observation is (in terms of standard deviation).

For instance, if z = 2, it means that the observation is 2 standard deviations higher than the mean.

Why Is Normal Distribution Important?

The normal distribution is important because it allows us to understand data variation through the simple concept. In addition, the normal distribution is strongly related to such basic concepts of statistics as estimation, hypothesis testing, confidence intervals, and sampling.

Nevertheless, it is essential to remember that not all datasets are normally distributed. They can be skewed, have outliers or several peaks. Therefore, it is better to examine data before making conclusions about its distribution.

Conclusion

The normal distribution is not only a bell curve presented in a textbook on statistics; it offers an effective tool that enables to comprehend how the values are distributed around the mean.

For students studying computer science, knowledge of the normal distribution becomes a cornerstone in comprehending probability, statistics, data science, and machine learning.

In other words, the normal distribution enables us to understand what is common, what is unusual, and how the observations are spread around the mean.