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Index Number and Reference Value

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Source: Milk photo taken by J. Gearin

This tutorial talks about index numbers and reference values. So first, we'll start with some examples of how these get applied. One thing you might have heard before is someone talking about how $1,000 1980, or some year in the past, are worth $2,789 in 2012. It's a way of comparing old weight to new money-- or the idea of the cost of inflation and finding a savings account to cover for that or the cost of living adjustments that get added for Social Security or someone saying that it hasn't been added since 2008. So let's look at how these things get calculated and where they come from.

So first, we talk about inflation. Inflation is a relative change in price. So with all relative changes, we're doing the same kind of set of calculations. It's the absolute change divided by the previous value. So if we're talking about the inflation in the cost of milk from 2007 to 2012, the old price in 2007 was $1.54, and the new price in 2012 was $2.24.

So here's what our calculation would look like. We would do the new value, $2.24, subtract the old value, $1.54, and divide by $1.54. So let's get a calculator to do that with. Us so $2.24 minus $1.54 gets us 0.7. Then divide by $1.54 gets 0.4545 repeating. So we can round this to 0.45, or 45%. That is our inflation. It's telling us how much prices have gone up by, how much we've increased by.

Now, there's also this idea of a reference value. And we use this when we're calculating index numbers. So a reference value is the measurement from a particular time or place that's chosen as the basis for comparison. It's also called the base year. So if you study economics, it's more commonly referred to as the base year. But reference value and base year are referring to the same thing.

So when we're calculating an index number, first we start by picking a value. Then divide it by the reference value and multiply it by 100. If the results you get is higher than 100, then the relative values have gone up. If the result is lower than 100, then the relative values have gone down.

So let's try that here. So we're going to calculate an index number for those same milk prices that we saw before. So first we need to pick a value. We need to pick our reference value. So we're going to pick the older value here. That's our reference value. And we also need to look at one of the newer values. So this is our new value. So we're going to take this value and divide by our reference value.

So we're going to have $2.24 divided by $1.54. And then multiply it by 100. So again, we'll get our calculator out. 2.24-- whoops. 2.24 divided by 1.54 and then multiply by 100.

So here, we get 145. And we need to evaluate this. So if we look at our old slide, we can see that if the result is higher than 100, then the relative values have gone up. And if it's lower than 100, then the relative values have gone down. So our result of 145 here means that the relative values have gone up.

Now, one application of index numbers and reference values is the Consumer Price Index. It's something that's calculated by the Bureau of Labor Statistics. They start by collecting a lot of data on the cost of goods and services and then compare them. And by doing those comparisons, they're able to measure inflation by calculating an index number. So these idea of index numbers and inflation all connect, and you need the reference values in order to calculate your index number. So this has been your tutorial on index numbers and reference values.