<p>When creating any index the base year is just year of which quantity is used to divide all other quantities. Hence general formula for index number for a random observation <span class="math-container">$X_i$</span> with base <span class="math-container">$n$</span> is simply:</p>
<p><span class="math-container">$$Index = \frac{X_i}{X_n}$$</span></p>
<p>This sort of transformation preserves the rates of change since:</p>
<p><span class="math-container">$$\frac{\frac{X_t}{X_n}- \frac{X_{t-1}}{X_n}}{\frac{X_t}{X_n}} = \frac{X_t- X_{t-1}}{X_t} $$</span></p>

CC BY-SA 4.0
2024-02-22T00:15:14.900Z
2024-02-22T00:15:14.900Z
1muflon1
<p>I was trying to understand inflation calculations when i came across this <a href="https://media.discordapp.net/attachments/1013422912344170497/1209998341585375242/image.png?ex=65e8f5c5&amp;is=65d680c5&amp;hm=812bb6b0b574dec08efe555035dc9df0fccf47c093a23f5a74de3f641a91848f&amp;=&amp;format=webp&amp;quality=lossless" rel="nofollow noreferrer">Scenario</a>, they are trying to calculating the 12 month inflation rate , but the weighted figures given(essentially percentage multipliers ), both have a base year of 2002 .</p>
<p>So when trying to calculate the 12 month inflation rate over that period they found the percentage change between the two weighted figured ,while this is correct ,mathematically i dont understand how this works as in this isnt something that would intuitively come to me and i still dont logically understand why this actually works and shows the percentage change in between in actuall prices between these 2 points in time .</p>
<p>If someone could layout a step by step mathematical working out, as to why this make sense , id be grateful as im really trying to visualise what happens to &quot;proportionality&quot; here  for this method to work ,as i completely lost track.</p>

<inflation>
Methods of calculating 12 month Inflation rates
user42141
# Methods of calculating 12 month Inflation rates

(Asked by: username_0 on 2024-02-21)

I was trying to understand inflation calculations when i came across this [Scenario](https://media.discordapp.net/attachments/1013422912344170497/1209998341585375242/image.png?ex=65e8f5c5&is=65d680c5&hm=812bb6b0b574dec08efe555035dc9df0fccf47c093a23f5a74de3f641a91848f&=&format=webp&quality=lossless), they are trying to calculating the 12 month inflation rate , but the weighted figures given(essentially percentage multipliers ), both have a base year of 2002 .

So when trying to calculate the 12 month inflation rate over that period they found the percentage change between the two weighted figured ,while this is correct ,mathematically i dont understand how this works as in this isnt something that would intuitively come to me and i still dont logically understand why this actually works and shows the percentage change in between in actuall prices between these 2 points in time .

If someone could layout a step by step mathematical working out, as to why this make sense , id be grateful as im really trying to visualise what happens to "proportionality" here for this method to work ,as i completely lost track.

**Tags:** inflation


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## 1 answers

### Answer by username_1 on 2024-02-22. Score: 1

When creating any index the base year is just year of which quantity is used to divide all other quantities. Hence general formula for index number for a random observation $X\_i$ with base $n$ is simply:

$$Index = \frac{X\_i}{X\_n}$$

This sort of transformation preserves the rates of change since:

$$\frac{\frac{X\_t}{X\_n}- \frac{X\_{t-1}}{X\_n}}{\frac{X\_t}{X\_n}} = \frac{X\_t- X\_{t-1}}{X\_t} $$


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