An intro to the Normal Distribution [Math Mondays]
One of the most important concepts that you will come in the software engineering.
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The normal distribution.
If there was a mount rushmore of Math Concepts, this would be a first-draft pick. The normal distribution shows up in so many problems and in so many ways that they literally called it the normal distribution.
It’s so common that chances are you use it all the time- often without realizing it. And given all the conversations I’ve had with people looking to use Data in their company processes, this idea will only become even more important. In this newsletter, we'll discuss the normal distribution, why it's important, and how it shows up in software development/tech.
The Normal Distribution 101
What is the normal distribution- I could give you the mathematical definition, but that’s not the most important for our case. For us, it’s important to understand that the normal distribution is a probability distribution that is often used to model real-world data. It is bell-shaped, with the mean, median, and mode all located at the center. The curve is symmetrical, so the area under the curve to the left of the mean is equal to the area under the curve to the right of the mean.
Why is the Normal Distribution Important: The Normal Distribution is important because it is a very common distribution for real-world data. It is used in a wide variety of fields, including statistics, engineering, and finance. It’s used to model grades in a class, costs of operation, job satisfaction, and much more. It can also be used to calculate probabilities, such as the probability that a random variable will fall within a certain range.
Why you should care: In software, we often rely on approximations and simplifications based on our needs. Creating the theoretically optimal solution might not be feasible, so you would often rely on shorthand to build something. Using a basic normal distribution to model future load/performance can be very useful to make the right sacrifices. If you have a large number of independent observations their mean will approximately have a normal distribution. Here are some examples to make things less abstract:
Estimating the time it takes for a program to run. The normal distribution can be used to estimate the average run-time of the program+ the standard deviation of the running time. This information can be used to set performance expectations, allocate resources, and identify avenues for improvement.
Estimating the number of errors that will occur in a program. The normal distribution can also be used to estimate the average number of errors that will occur in a program.
Estimating the number of users who will encounter a particular bug. We can also use it to estimate the average number of users who will encounter a particular bug, This information can be used to set risk expectations for the program and to identify areas where the program can be improved. If we see that the ROI of fixing a bug is not worth it (the costs of fixing the bug are high, and users who will deal with it are low), the optimal solution might just be to ignore this. This technique has a full Wikipedia dedicated to it, called the Ostrich algorithm.
This is one of the most important concepts that you should add to your tool belt. Highly recommend studying this idea to learn more. To those of you that exploring ideas in more details, I’m liking a beautiful video by 3Blue1Brown (
) . His video is great because it tells us a very interesting story about this amazing distribution, one that will help you appreciate the beauty of normal distributions more.That is it for this piece. I appreciate your time. As always, if you’re interested in working with me or checking out my other work, my links will be at the end of this email/post. If you like my writing, I would really appreciate an anonymous testimonial. You can drop it here. And if you found value in this write-up, I would appreciate you sharing it with more people. It is word-of-mouth referrals like yours that help me grow.
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