Statistical interview question: give an example of a random variable that follows a normal distribution
The normal distribution, often called the Gaussian distribution, is widely considered the most common distribution in statistics and many other fields.It is frequently used to model real world data and is essential for many statistical procedures.
The normal distribution is bell shaped and is characterised by two parameters, being the mean and the standard deviation.
The mean is the average of all of the data points and is the central point of the distribution.
The standard deviation tells the scientist how spread out the numbers are around the mean in a dataset, revealing how much the data varies from the mean. It plays a crucial role in determining the shape and spread of the distribution.
The standard deviation measures the distance between each data point from the mean. It determines the width of the bell curve:-
- A smaller standard deviation means that the data points are closer to the mean, resulting in a narrower bell curve.
- A larger standard deviation means the data points are spread out, resulting in a wider bell curve.
The normal distribution is symmetrical, with most of the data clusters centering around the mean, or average.The normal distribution follows the empirical rule, where 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.
A special case of the normal distribution is where the mean is 0 and the standard deviation is 1. It is often used in statistical calculations and is represented by the z-score.
The normal distribution is a type of continuous probability distribution for a real valued random variable. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real valued random variables whose distributions are not known.
The formula for the normal distribution is:-
A classic example of a random variable following a normal distribution is the human height. The heights of individuals in a population tend to cluster around the average height, with fewer people being extremely tall or extremely short. The clustering around the average, where most observations fall, and the tapering off of the extremes, is a characteristic of the normal distribution.
The python code below is an example of who the heights of men tend to follow a normal distribution:-
