Solve each problem. The table lists how poverty level income...

Solve each problem.
The table lists how poverty level income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the poverty level cutoff in 2012 to the nearest dollar.
(TABLE CANNOT COPY)

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Key Concepts

Linear Interpolation

Linear interpolation involves estimating a value within two known values in a data set by assuming the change between these values follows a linear pattern. This technique allows one to predict intermediate points based on a straight-line connection between existing data points, making it a practical method for approximating values that are not directly provided.

Midpoint Formula

The midpoint formula is a mathematical tool used to determine the value that lies exactly halfway between two given numbers. It is calculated by taking the sum of the two numbers and then dividing that sum by two. This approach is useful in various contexts when an average value or a central point in a range is needed.

Transcript

00:01 This problem uses the midpoint formula again to ask us to estimate, in this case, the poverty -level income cutoffs for a family of four in the year 2012.

00:13 So we don't know the number for 2012.

00:15 That's not provided to us in the table.

00:17 If so, this would be a very easy problem.

00:19 It'd just be copied down the number.

00:21 In this case, we have numbers for five different years here, 1990, 2010, 2011, and 2013.

00:30 And we need to find what it is, estimate what it is for 2012.

00:35 So to do this, we need to figure out which of these years that are listed over here would give us what we need, would be the average.

00:44 When you add the two years together, would average out to be 2012.

00:48 So this should be a fairly simple one just to look at, and you don't even necessarily need to mathematically calculate this one.

00:55 Hopefully it's fairly simple to know that 2011 and 2013 are our answers here because in between those two, you have 2012.

01:04 In fact, right in between it.

01:06 So that's exactly what we're looking for here.