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
pie
title Commodities Purchase Distribution
"100 tonnes at £70" : 100
"300 tonnes at £80" : 300
"50 tonnes at £95" : 50
Exercise Room (aka Quiz Time!)
Time to flex those brain muscles with some quirky questions!
### What does the weighted average consider that a simple average does not?
- [ ] The lighter side of a balanced diet
- [x] The importance of items
- [ ] Quantities of items only
- [ ] Random item prices
> **Explanation:** A weighted average carefully considers the importance (weights) of each contributing item rather than treating each item as equal.
### In the given example, what was the total weight used to calculate the weighted average?
- [ ] 100 tonnes
- [ ] 300 tonnes
- [x] 450 tonnes
- [ ] Nothing was weighed
> **Explanation:** Sum up all the tonnes: 100+300+50 = 450 tonnes, which is the total weight in the weighted average calculation.
### If you ignore the weights in calculated example, what incorrect average would you get?
- [ ] £80
- [ ] £79.44
- [ ] £70
- [x] £81.7
> **Explanation:** A simple average would misguidedly lead you to (70 + 80 + 95)/3 = £81.7.
### What is the main utility of using weighted averages in finance?
- [ ] To balance financial seesaws
- [ ] To calculate simple values
- [x] To get accurate representations of data
- [ ] To confuse accountants
> **Explanation:** Weighted averages help in providing accurate data representations considering the importance of various values.
### What would the correct weighted average be if the prices were weighted by quantities according to the example?
- [ ] £70
- [x] £79.44
- [ ] £81.7
- [ ] £80
> **Explanation:** Using the weighted average formula, it turns out to be approximately £79.44.
### Imagine you bought 200 tonnes at £60, 100 tonnes at £90, and 200 tonnes at £70. What should the first step be?
- [ ] Calculate simple average
- [x] Find total weights
- [ ] Leave it unfinished
- [ ] Contact a psychic accountant
> **Explanation:** First, find the total weights to set the ground work for weighted average calculation.
### Weighted averages apply to only financial data. True or False?
- [ ] True
- [x] False
> **Explanation:** Weighted averages can be usefully applied in various fields beyond finance, such as education, research, and sports metrics.
### Why might simple averages sometimes be misleading?
- [ ] Because they like causing trouble
- [x] They ignore item importance
- [ ] They are complicated
- [ ] They need weights
> **Explanation:** Simple averages disregard the significance (weights) of each value, leading to potentially skewed results.
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