📊 Weighted Average: Carrying the Heavyweights!

Overview§

Ever wondered how numbers get their bling on? Step right up and meet the world of Weighted Averages! It’s the arithmetic Ferris wheel where not all numbers are created equal. Some numbers munch power bars and lift heavier weights, while others just sip lattes.

🎢 The Roller Coaster Ride§

Imagine you’re a trader on a shopping spree. But you’re not just bagging random items like a sleep-deprived shopaholic; instead, you’re meticulously picking items with diverse price tags and quantities. Here’s how our numbers perform their yoga:

The Scenario:

• 100 tonnes bought at £70 per tonne
• 300 tonnes bought at £80 per tonne
• 50 tonnes bought at £95 per tonne

Perfectly simple arithmetic will tell you, “Hey, just average them out!” (70 + 80 + 95)/3 = £81.7. Hold your calculators because the simple average isn’t smart enough for this premium ride. Let’s jazz it up to the weighted average:

🎯 Calculating Weighted Average§

This bad boy is all about weights and balances:

$$Weighted Average = \dfrac{(70 \times 100) + (80 \times 300) + (95 \times 50)}{100 + 300 + 50}$$

Now dissect that! Each price is multiplied by the quantity and then divided by the total quantity, instead of just chillin’ out there on its own.

Let’s break it down:

$$Weighted Average = \dfrac{(7000 + 24000 + 4750)}{450} = \dfrac{35750}{450} \approx £79.44$$

✨ Ta-Da! The actual Weighted Average is a neat £79.44. (cue imaginary applause)

📉 Why Use Weighted Average?§

Life Lesson: In the Land of Numbers, everyone deserves their share of glitter. Weighted averages help investors, accountants, and nosey parkers get an accurate representation of data. So whether you’re indexing share prices or debate club scores, this formula’s your go-to buddy.

Mermaid Markdown Showdown§

Exercise Room (aka Quiz Time!)§

Time to flex those brain muscles with some quirky questions!