The normal distribution is widely used in understanding distributions of factors in the population. Because the normal distribution approximates many natural phenomena so well, it has developed into a standard of reference for many probability problems.
Normal/Gaussian Distribution is a bell-shaped graph that encompasses two basic terms- mean and standard deviation. It is a symmetrical arrangement of a data set in which most values cluster in the mean and the rest taper off symmetrically towards either extreme. Numerous genetic and environmental factors influence the trait.
Central Limit Theorem
Normal distribution follows the central limit theory which states that various independent factors influence a particular trait. When these all independent factors contribute to a phenomenon, their normalized sum tends to result in a Gaussian distribution.
Normal Curve
The mean of the distribution determines the location of the center of the graph, the standard deviation determines the height and width of the graph and the total area under the normal curve is equal to 1.
Let’s understand the daily life examples of Normal Distribution.
1. Height
The height of people is an example of normal distribution. Most of the people in a specific population are of average height. The number of people taller and shorter than the average height people is almost equal, and a very small number of people are either extremely tall or extremely short. Several genetic and environmental factors influence height. Therefore, it follows the normal distribution.
2. Rolling A Dice
A fair rolling of dice is also a good example of normal distribution. In an experiment, it has been found that when a dice is rolled 100 times, chances to get ‘1’ are 15-18% and if we roll the dice 1000 times, the chances to get ‘1’ is, again, the same, which averages to 16.7% (1/6). If we roll two dice simultaneously, there are 36 possible combinations. The probability of rolling ‘1’ (with six possible combinations) again averages to around 16.7%, i.e., (6/36). More the number of dice more elaborate will be the normal distribution graph.
3. Tossing A Coin
Flipping a coin is one of the oldest methods for settling disputes. We all have flipped a coin before a match or game. The perceived fairness in flipping a coin lies in the fact that it has equal chances to come up with either result. The chances of getting a head are 1/2, and the same is for tails. When we add both, it equals one. If we toss coins multiple times, the sum of the probability of getting heads and tails will always remain 1.
4. IQ
In this scenario of increasing competition, most parents, as well as children, want to analyze the Intelligent Quotient level. Well, the IQ of a particular population is a normal distribution curve; where the IQ of a majority of the people in the population lies in the normal range whereas the IQ of the rest of the population lives in the deviated range.
5. Technical Stock Market
Most of us have heard about the rise and fall in the prices of shares in the stock market. These changes in thelog valuesofForexrates, price indices, and stock prices return often form a bell-shaped curve. For stock returns, the standard deviation is often called volatility. If returns are normally distributed, more than 99 percent of the returns are expected to fall within the deviations of the mean value. Such characteristics of the bell-shaped normal distribution allow analysts and investors to make statistical inferences about the expected return and risk of stocks.
6. Blood Pressure
Blood pressure generally follows a Gaussian distribution (normal) in the general population, and it makes Gaussian mixture models a suitable candidate for modelling blood pressure behaviour.
7. Shoe Size
Have you wondered what would have happened if the glass slipper left by Cinderella at the prince’s house fitted another woman’s feet? He would have ended up marrying another woman. It has been one of the most amusing assumptions we all have ever come across. As per the data collected in the US, female shoe sales by size are normally distributed because the physical makeup of most women is almost the same.
8. Birth Weight
The normal birth weight of a newborn ranges from 2.5 to 3.5 kg. The majority of newborns have normal birthweight whereas only a few percent of newborns have a weight higher or lower than normal. Hence, birth weight also follows the normal distribution curve.
9. Student’s Average Report
Nowadays, schools are advertising their performances on social media and TV. They present the average result of their school and allure parents to get their children enrolled in that school. School authorities find the average academic performance of all the students, and in most cases, it follows the normal distribution curve. The number of average intelligent students is higher than most other students.
FAQs
What are some real life examples of normal distributions? In a normal distribution, half the data will be above the mean and half will be below the mean. Examples of normal distributions include standardized test scores, people's heights, IQ scores, incomes, and shoe size.
What are examples of things that closely follow a normal distribution? ›
Many everyday data sets typically follow a normal distribution: for example, the heights of adult humans, the scores on a test given to a large class, errors in measurements.
What is an example of a normal distribution in psychology? ›
An IQ (intelligence) test is a classic example of a normal distribution in psychology. Most people tend to have an IQ score between 85 and 115, and the scores are normally distributed. Height, shoe size or personality traits like extraversion or neuroticism tend to be normally distributed in a population.
What are some examples of quantities that are typically normally distributed? ›
Approximately normally distributed quantities are height and weight are approximately distributed. Variation in the rate of return in some financial instruments are normally distributed. Einstein showed that the kinetic energy of individual molecules in a perfect gas is normally distributed.
What is an example of a distribution in real life? ›
Uniform distribution: A deck of cards also has a uniform distribution. This is because an individual has an equal chance of drawing a spade, a heart, a club, or a diamond. Another example with a uniform distribution is when a coin is tossed. The likelihood of getting a tail or head is the same.
What is normal distribution with example? ›
Normal Distribution Curve
The random variables following the normal distribution are those whose values can find any unknown value in a given range. For example, finding the height of the students in the school. Here, the distribution can consider any value, but it will be bounded in the range say, 0 to 6ft.
Which example would fit the normal distribution? ›
Example of a Normal Distribution
Taller and shorter people exist with decreasing frequency in the population. According to the empirical rule, 99.7% of all people will fall with +/- three standard deviations of the mean, or between 154 cm (5' 0") and 196 cm (6' 5").
Why are some things normally distributed? ›
The Normal Distribution (or a Gaussian) shows up widely in statistics as a result of the Central Limit Theorem. Specifically, the Central Limit Theorem says that (in most common scenarios besides the stock market) anytime “a bunch of things are added up,” a normal distribution is going to result.
How do you show something is a normal distribution? ›
A normal distribution has some interesting properties: it has a bell shape, the mean and median are equal, and 68% of the data falls within 1 standard deviation.
What is an example of a normal distribution in healthcare? ›
Blood pressure has a normal distribution: if you if you plot values of systolic blood pressure on the x-axis and the number of people with that blood pressure on the y-axis, you get a bell-shaped curve as shown in this figure. The mean corresponds to the peak of the curve.
Normal Distribution Examples
Example 1: Standardized Tests. The results of a standardized test will follow a normal distribution. The average test score will be the midline and peak of the bell curve.
What is an example of a normal distribution of grades? ›
All things being equal, if grades are normally distributed, about 2% of the students will receive an A, 14% will get a B, 68% get Cs, 14% get Ds, and 2% of the class get an F. Essentially, 84% of the grades would be Cs, Ds, and Fs.
What is normally distributed in real life? ›
All kinds of variables in natural and social sciences are normally or approximately normally distributed. Height, birth weight, reading ability, job satisfaction, or SAT scores are just a few examples of such variables.
What is a real life example of a bell curve? ›
A bell curve is used to make life easy. In general, if a scientist randomly sampled 100 people, they would find that their results follow a normally distributed curve for many variables, like height, weight, blood pressure, and other vital signs, or norms for that person, as one example.
When to use normal distribution? ›
Making inferences about populations. If you have a sample of data from a population that is normally distributed, you can use the normal distribution to make inferences about the population as a whole. For example, you could use the normal distribution to estimate the mean or standard deviation of the population.
What is a real life example of normality? ›
For example, “Height of people” is something that follows a normal distribution pattern perfectly: Most people are of average height, the numbers of people that are taller and shorter than average are fairly equal and a very small (and still roughly equivalent) number of people are either extremely tall or extremely ...
What is sample distribution in real life example? ›
Practical Example
You take random samples of 100 children from each continent, and you compute the mean for each sample group. For example, in South America, you randomly select data about the heights of 10-year-old children, and you calculate the mean for 100 of the children.
What are the main applications of normal distribution? ›
Normal distribution is used in various fields to model the behavior of random variables. Some of its applications are as follows: In finance, normal distribution is used to model the behavior of stock prices, interest rates, and other financial variables.
Why normal distribution is important in our life? ›
As with any probability distribution, the normal distribution describes how the values of a variable are distributed. It is the most important probability distribution in statistics because it accurately describes the distribution of values for many natural phenomena.