Three Math Concepts You’ll Actually Use in the Real World
“You’ll never use that in the real world anyway”
When I was studying math in high school and college, I always heard people say things like that. While it’s true that I’ve never actually factored another polynomial, applied the Pythagorean theorem, or calculated another analytic derivative or integral, etc., I’m sure at multiple points in my career, I somehow already felt the edge of being a Math lover.
It’s difficult to describe, but practising Math helped me solve problems in ways I believe everyone (and not just technical people) would benefit from.
My goal in this post is to share three basic math concepts we learned in the classroom that I believe everyone will find useful applying in the real world. These are concepts I use on a daily basis (as a data professional), and some of us also probably already use them without realizing it. I believe recognizing and mastering these will show how (1) math is useful beyond the classroom and (2) that math is everywhere in the real world.
Math Concept #1: Venn Diagrams
Who doesn’t love Venn Diagrams?
They’re so flexible that they can be used for a variety of use cases ranging from funny memes, all the way to mediums for teaching life lessons.
The concept of Venn Diagrams is usually encountered during our time in the classroom, most probably when studying Set Theory (Recall: unions, intersections, etc.).
In some form or another, I’m sure all of us have encountered a question like the following: “If all A’s are B, are some A’s are C’s then are some B’s also C’s?” These are called syllogisms — and it can easily get confusing if we don’t have the proper tools to deal with them. Problems like these are actually hidden in plain sight in the real world:
Real World Applications
- In the pandemic, how many people got tested? Out of those who tested positive, how many are actually negative? What percent of people who tested negative are actually positive? (i.e. Confusion Matrices)
- Of those people who saw your Facebook ad, how many actually signed up for an account? How many people actually bought your product without seeing the ad? How many saw the ad, was referred by a friend, but did not buy? (i.e. Conversion funnels — especially non-linear customer journeys).
- If we’re going to give vaccines to front liners first, then those at risk, then dependents, and so on, how many vaccines do we need in total for the first batch, 2nd, and so on, without double counting? Consider that these groups may not be mutually exclusive! (i.e. counting problems, or operations research)
It’s easy to be confused when trying to navigate the examples above, especially when you try to do them mentally. In my career, there have been many cases where a meeting went into circles because people can’t seem to get to the same page dealing with a problem like above.
Thankfully, when I encounter problems like these, my math instincts immediately tell me to whip up a piece of paper, draw the relevant circles, and create Venn Diagrams to make things clearer. A short explanation later, we then are able to pinpoint each area of the Venn Diagram, identify how many entities are involved, and decide as a group on what’s the appropriate strategy!
For those who did not buy our product but saw the ad, we could try a different sales approach. Those who tested negative for the virus but were actually positive tells us the effectiveness of a testing kit. For the first and 2nd batch of vaccines, we may need 100 doses each, but the 3rd, we may not need 100 again since these individuals already qualified in the 1st or 2nd batch.
Venn Diagrams are like the Swiss army knife for logic problems. Mastering when and how to use them will do you wonders not just in your career but everywhere else.
Math Concept #2: Distributions
I encountered this tweet before:
This isn’t a data post, but I suppose I can build on what I believe to be the message of the tweet above to explain the importance of distributions.
Let’s say we wanted to understand wealth distribution. Below is a graph showing how many people belong in each income bracket in the Philippines from a 2018 survey:
Suppose the goal is to understand the state of income inequality. A straightforward conclusion from the chart is that most people earn between around $220 — $438 per month, while a few people enjoy somewhere north of $4382 per month (around 10x higher!). If you know a bit of statistics, you can compute that the weighted average income is somewhere higher than $438 per month. You might even try to get the median and mode… and oh, even the 10th and 90th percentiles! Wait.. what were we trying to do again?
Things can easily get complicated the moment we dive deep to statistics. The difference is that with an experienced statistician, he or she looks at the distribution, makes a few calculations, and says something as simple as “around 25% of the wealth of the country is allocated to 5% of the entire population”
I probably digressed at this point but this altogether stresses the importance of mastering the concept of distributions. In my teaching experience, distributions are one of the most commonly misunderstood topics in mathematics, yet it remains one of the most used in practice!
Real World Applications
- What age ranges can we see the highest number of fatalities for the pandemic? How about the highest number of infections? (You’ll easily find these questions have different distribution shapes — and of course this leads to different strategies in developing health protocols)
- What’s the usual number of seconds until people lose interest in a certain video? (How long should Instastories or TikTok videos last?). How about the usual number of ads we tolerate before we close our social media apps? (Setting limits to the number of ads shown).
- Which locations contain the highest density of traffic activity as detected in navigation apps? (Imagine heatmaps) In which areas should we apply bike lanes, or deploy more traffic officers?
The moment you hear words or phrases like “usual”, “average”, “most or least common”, and other synonyms, you know you’ve encountered a problem involving a distribution.
Mastering distributions means recognizing that there are phenomena in the world more than the usual bell-shaped normal distribution. A distribution can be discrete or continuous, skewed or symmetric, unimodal or multimodal (has two or more ‘peaks’), and a lot more. Statistics like means or medians help in capturing some of the info, but more often than not, you would want to see the entire story.
If you want to dive deeper, there’s a lot of posts exploring distributions and their applications like the one below by Michał Oleszak:
Math Concept #3: Ratios
I personally call ratios the ‘great equalizers of mathematics’ in relation to how they’re commonly used in practice.
To illustrate with a quick example (and I’m probably overusing the topic of the pandemic by now), let’s take a look at the numbers below from the WHO website showing the number of cumulative Covid-19 cases per country.
From here, the first mistake that one can make is assume that the worst performing country with the pandemic response is the USA, followed by Brazil and India. However, I’m sure most people will understand this is an unfair way to assess each country, since it’s really not an apples to apples comparison. Each country has a different population number — if there’s more people, then of course there’s more cases!
Using a simple ratio, cases per 100,000 people (i.e. out of 100,000 individuals, how many on average got the disease?), we can then ‘equalize’ the landscape and compare across different countries.
Well, the USA is still the highest, but at least this reveals that India is actually showing a lower ratio in comparison to the other countries (Disclaimer: there are many ways to assess Covid response performance — this is one example among many other factors).
Ratios are probably even more common in application than Distributions and Venn Diagrams. More than being ‘great equalizers’, they also summarize information (think X out of 10 infographics, percentage statistics), translate between units (think Forex or converting between metric systems), and many more. There’s really so many applications that I would probably need an entire new post to list down some of the most important ones.
Real World Applications
- Where should I invest in? A stock that can go to $30 to $40 ($10 difference), or a stock that can go from $40 to $52 ($12 difference)? (percent changes are also ratios!)
- An email campaign that got 100 new users for a consumer product (large base) vs another email campaign that got 100 new users for a corporate product (small base), which is arguably better if emails have the same cost?
- Suppose we have data from transportation apps and we have total distance and time travelled by all cars in every area, can we get a measure of ‘how bad traffic is’ across different locations? (Think speed, another ratio, as a proxy for traffic).
Like the other concepts, mastering when and how to use ratios is one of the most helpful skills you can learn. It can start with familiarizing yourself where they’re best used such as comparisons, measuring relative change vs absolute change, translating units of measurement, and other common applications. The next thing you know, you’re almost always ordering the larger sizes of pizzas, knowing they offer the best value for money (depends on the restaurant).
Opinion: Modern Education should focus on Logic, Basic Statistics, and Coding
As a final take before ending this post, I want to share an article from 2019 that my friend shared with me while I was in the process of making this entry. Here’s a direct quote from the post:
Our high school students are taught algebra, geometry, a second year of algebra, and calculus (for the most advanced students) because Eisenhower-era policymakers believed this curriculum would produce the best rocket scientists to work on projects during the Cold War.
One of the most striking notes shared is that most of the modern day curriculum hasn’t changed for over 50 years, despite the drastic change in our capabilities to process information with the rise of computers.
We are now in the information era where the amount of data grows faster than the capability of humans to process its entire complexity. Because of this, what I’ve observed is that problems are becoming more and more biased towards “what data should we look at” and “how should we look at it?” over “how do we extract insight from limited data?”
I’m not saying Calculus and the like should be thrown out the window (I still love them!), but definitely there is the case to be made that everyone should consider going deeper into Logic, Basic Statistics, and Coding. In some form or another, the three math concepts discussed touch on these three subjects (coding makes it easier and faster). I genuinely believe this doesn’t just apply to technical practitioners like myself, but to anyone who touches numbers and data.
I do hope in the future, we live in a world where “You won’t apply that in the real world anyway” would finally become an outdated statement!
This post is mostly an amalgamation of thoughts I’ve formed as a data professional with the heart of a Mathematics Major. Please feel free to shoot an email to nfrimando@gmail.com or connect with me via LinkedIn. Glad to share notes and discuss should you have thoughts and comments to share! Shout out *again* to Fernandina Ko who helped me edit this piece!
