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Index Number and Reference Value

Index Number and Reference Value

Author: Ryan Backman

Identify index numbers from a reference value.

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Hi, this tutorial covers the ideas behind an index number and a reference number. So let's start with looking at an interesting example of where an index number has been used. So The Economist, which is an economics magazine or journal, has often published what are called Big Mac indexes, so the Big Mac being the McDonald's hamburger. And they did that as a way to compare US purchasing power in other countries around the world.

So since most countries have McDonald's and sell Big Macs, they're looking at just comparing the different prices of Big Macs in different countries. So the average price of a Big Mac in the US in January, 2012 was $420-- excuse me. $4.20. The average price of a Big Mac in Norway is $6.79, and in Thailand it is $2.46. So both of these two prices were converted from the native currencies to US dollars.

So the Big Mac index for Norway is 161.7, and the Big Mac index for Thailand is 58.6. So what you want to do with these two numbers is compare them to the number 100. 100 is the magic number. So a number bigger than 100 means that that country is more expensive than the US, and a number under 100 means that it would be less expensive than the US. So Norway is known to be a pretty expensive country, and then Thailand is going to be a country that's going to be less expensive. So US citizens are going to have less purchasing power in Norway and more purchasing power in Thailand.

So let's take a look at these two numbers and see how they were calculated. So they were both index numbers. An index number is a number calculated to compare measurements taken at different places or different times. So in this case, we're looking at different places, different countries. And then a reference number is a value of one particular time or place used to calculate an index number. So since we're since The Economist is a US publication, they're using the US Big Mac price as the reference number.

So to calculate an index number, you simply take the new value divided by the reference value, and then you multiply that number by 100. So let's go back and take a look at how the two index numbers were calculated, so the 161.7 and the 58.6. So let's go ahead and do those calculations for both Norway and for Thailand.

So for Norway, again, it's going to be the new value, divided by the reference value, times 100. So the new value being the price of the Big Mac in Norway. Your reference value is the Big Mac price for the US. And then you want to multiply that number by 100. OK, so if we calculate that ratio, so dividing those two numbers in our calculator and then multiplying that by 100 and rounding that value, we end up with 161.7, again, that being our Big Mac index for Norway.

Now, if we look at Thailand, again, it's going to be your new value, divided by your reference value, times 100. So in this case, we're going to take the price of the Big Mac in Thailand, divided by our reference value, and multiply that by 100. So again, if we go into the calculator, I'm going to do 2.46 divided by 420-- excuse me, $4.20, and then multiply that number by 100. And I end up with 58.6 as my index number. So that is how you those two index values were calculated for the two different countries.

All right, an index can also be used to measure inflation, so not only just purchasing power but also inflation. So inflation is a rise in the prices of goods or services in an economy over time. So let's take a look at an example of how inflation is commonly measured. So suppose a gallon of milk increases from $4 to $5 over three years. The inflation here can be quantified in two ways, as relative change or as an index. So what we're going to do is calculate the inflation of this gallon of milk in these two ways. So let's start with relative change.

So with relative change, remember, what you do for that is you take your new value, subtract the old value, and you divide by the old value. So we have 5 minus 4, divided by 4. So if we do that, that ends up being 1 over 4. So 1/4 then as a decimal is 0.25. And relative change is generally expressed as a percent, so that's going to end up being 25%. So what that means is that over these three years, the price of milk increased by 25%.

Let's also do this as an index. So remember, when you're calculating an index, you take your old value divided by your new value. So what we're going to do is we're going to take the new value divided by the old value, so 5 divided by 4. Then we multiply by that reference value of 100. So 5/4, if you divide those two, you end up with 1.25. So it's 1.25 times 100, which ends up being 125. So since that 125 is bigger than your reference value of 100, that means that you do have some inflation in the price of milk here. So again, that's two ways of expressing inflation of this gallon of milk over the three years, both in terms of a percent as relative to change, but also as an index value.

A common place where you see index values is what's known as the CPI which is the consumer price index. And what that is, is it's the weighted sum of the indexes of over 60,000 goods and services, and this is specifically for the US. And the US Bureau of Labor calculates the CPI frequently to measure inflation in the US. So suppose we were doing-- if we were going to calculate the CPI, maybe that gallon of milk would be one of the indexes that they're going to use to create the CPI. And it's a weighted sum, so that means that of all of these goods and services, different goods and services might have a different weight to them.

Now, what I have here is a graph of the average CPI and then the percent change of CPI. We're just going to concentrate on the average CPI which is this graph. So we can see, as the years increase, the CPI-- and notice right around the '70s That's when we started to see a large increase in CPI. In the mid 2000s, which is about where this is at, we can see that our CPI is almost up to-- it's probably at about 180, 190.

So again, comparing that to 100, 100 was '82 to '84. So we can see we're already up to about 180, so we have had considerable inflation. So CPI, again, is just one place where an index is used, in this case, to measure inflation. So that is the tutorial on an index number and reference number. Thanks for watching.

Terms to Know
Consumer Price Index

An index published by the US Bureau of Labor Statistics that shows the change in the price of many different goods or services in the United States. It provides a measure of purchasing power.

Index Number

A way to measure the relative change in a value, usually the price of a good or service, over time. If the index number is over 100, that means the price has increased. If the price has decreased, then the index number will be less than 100.


A relative increase in the price of a good or service over time. A person will need to pay more to receive the same good or service than they did at a previous point in time.

Reference Value

An arbitrarily chosen starting value for an index. It is assigned an index number of 100.

Formulas to Know
Index Number

fraction numerator n e w space v a l u e over denominator r e f e r e n c e space v a l u e end fraction cross times 100