[{"content":"Let\u0026rsquo;s Start With a Story Imagine you work at a café and earn $15 per hour. As you work more hours, the amount of money you earn grows as well. Every additional hour adds another $15 to your pay.\nMany situations in everyday life behave like this - when one thing changes, another changes alongside it in a steady and predictable way.\nThis idea is at the heart of what mathematicians call a linear function.\nSo What Is a Linear Function? A linear function describes a relationship between two things where the change happens at a constant rate. In other words, for every equal increase in one quantity, the other quantity changes by the same amount.\nYou may see it written like this: y = mx + b\nIf that expression looks unfamiliar, don\u0026rsquo;t worry about remembering it right now. The most important thing is understanding the idea behind it.\nLet\u0026rsquo;s look at each part using our café example.\nSymbol What It Represents Café Example y The result we want to know Total money earned x The amount we choose or change Hours worked this week m How much the result changes each time $15 earned per hour b What you already have before starting Money earned last week The b is easy to overlook, but it is important.\nImagine you already earned $60 last week. This week you work 3 hours at $15/hour.\nYour total is not just 3 x $15 = $45. It is $45 + $60 = $105.\nThat $60 is your b - your starting point before this week even begins.\nWhen b = 0, it simply means you are starting from nothing.\nTry It Yourself - The Café Calculator Play with the sliders below. Try setting last week\u0026rsquo;s earnings to $60 and see what happens to your total!\n☕ Your Café Earnings Calculator\n💰 Hourly rate (m) $15 ⏰ Hours worked (x) 1 hr 📦 Last week earned (b) $0 Your formula\ny = 15 x 1 + 0\nThis week\n$15\nLast week (b)\n$0\nTotal (y)\n$15\nWork 1 hour at $15/hr and you earn $15 this week. No savings from last week yet. Seeing the Pattern Suppose you earn $15 per hour with no carry-over from last week.\nHours Worked Money Earned 0 $0 1 $15 2 $30 3 $45 4 $60 Notice something - every time the hours increase by 1, the money earned increases by $15. The increase stays the same each time. That steady pattern is what makes this relationship linear.\nExplore Further - The Graph Builder Now that you understand the idea, try building your own linear function below. Watch how changing m and b affects the shape and position of the line.\n📈 Build Your Own Linear Function!\n⭐ Slope (m) 1 💜 Start point (b) 0 y = 1x + 0\nA slope of 1 means: for every 1 step right, the line goes 1 step up. A Helpful Way to Think About It A linear function is like walking up a staircase where every step has the same height. You always move upward by the same amount.\nBecause the change is consistent and predictable, linear functions are often used to model things such as:\nHourly wages Distance travelled at a constant speed Monthly savings Phone plans with a fixed cost per month Whenever a relationship grows or decreases at a steady rate, a linear function may be a useful model.\nKey Idea A linear function describes a relationship where the output changes at a constant rate as the input changes. The formula y = mx + b is simply a compact way of describing that pattern.\nBefore memorizing the formula, focus on recognizing the idea:\nEqual changes in the input produce equal changes in the output.\nQuick Quiz - Test Yourself! 🧠 Quick Quiz - Test Yourself!\n🔄 Try Again ","permalink":"https://ds-explained.pages.dev/posts/math/what-is-a-linear-function/","summary":"\u003ch2 id=\"lets-start-with-a-story\"\u003eLet\u0026rsquo;s Start With a Story\u003c/h2\u003e\n\u003cp\u003eImagine you work at a café and earn \u003cstrong\u003e$15 per hour\u003c/strong\u003e. As you work more hours, the amount of money you earn grows as well. Every additional hour adds another \u003cstrong\u003e$15\u003c/strong\u003e to your pay.\u003c/p\u003e\n\u003cp\u003eMany situations in everyday life behave like this - when one thing changes, another changes alongside it in a steady and predictable way.\u003c/p\u003e\n\u003cp\u003eThis idea is at the heart of what mathematicians call a \u003cstrong\u003elinear function\u003c/strong\u003e.\u003c/p\u003e","title":"What is a Linear Function?"},{"content":"Let\u0026rsquo;s Start With a Story Imagine a class has 10 students. Nine students scored 50/100 on a test. But 1 student is a genius and scored 100/100.\n🎯 Drag the outlier score and watch the magic happen!\n⭐ Outlier score 100 Data: 50, 50, 50, 50, 50, 50, 50, 50, 50, 100 💙 Mean (Average)\n55.0\nchanges with outlier\n💜 Median (Middle)\n50\nstays the same!\n🌟 The outlier pulls the mean up, but the median stays at 50 — where most students actually scored! But here\u0026rsquo;s the problem: almost everyone scored 50, not 55. The score of one exceptional student pulled the average higher than what most students actually achieved. So if you only looked at the average, you might get the wrong picture of the class.\nTwo Ways to Describe \u0026ldquo;Typical\u0026rdquo; There are two simple ways to find a \u0026ldquo;typical\u0026rdquo; number in a group:\n1. Mean (Average) Add up all the numbers, then divide by how many numbers there are. For our class, Mean = 55\n2. Median (Middle Value) Line up all the numbers from smallest to biggest, and pick the one right in the middle. For our class, Median = 50\nThe median tells us that a typical student scored around 50, which matches what most students actually got.\nWhy Does This Happen? The average gets \u0026ldquo;pulled\u0026rdquo; toward very high or very low numbers. One huge number (like 100) can drag the whole average up, even if everyone else scored much lower.\nThe middle value doesn\u0026rsquo;t care about how big or small the extreme numbers are - it just looks at where the \u0026ldquo;middle\u0026rdquo; of the group is.\nWhere You\u0026rsquo;ll See This in Real Life \u0026ldquo;Average salary at this company is $90,000\u0026rdquo; - but maybe the boss earns way more than everyone else, and most workers earn much less. \u0026ldquo;Average house price in this area is $1 million\u0026rdquo; - but a few giant mansions might be pulling that number way up. \u0026ldquo;Average screen time is 6 hours a day\u0026rdquo; - but maybe a few people use their phones 12+ hours, while most people use it for 2-3 hours. The Big Takeaway The mean (average) is useful, but it doesn\u0026rsquo;t always represent what\u0026rsquo;s typical.\nWhen data contains extreme values, the median often gives a clearer picture of reality.\nThat\u0026rsquo;s why data analysts don\u0026rsquo;t stop at the average - they look deeper.\nAnother Real-Life Example Still not convinced? Here\u0026rsquo;s the same idea with house prices:\nThe story is the same - one extreme value (the mansion!) pulls the mean up, while the median stays where most houses actually are.\n🧠 Quick Quiz — Test Yourself!\n🔄 Try Again 📸 Prefer learning visually? Follow @data.madesimple on Instagram - where we turn complex data concepts into cute, easy-to-understand visuals. 🐧📊\n","permalink":"https://ds-explained.pages.dev/posts/statistics/why-average-can-lie/","summary":"A simple look at why \u0026lsquo;average\u0026rsquo; doesn\u0026rsquo;t always mean what you think it means.","title":"Why the Average Can Lie to You"}]