# #23 – What’s Interpolation? Our 5-minute Crash Course on Graph Analysis

Imagine looking at your watch but not knowing how to read the time. Or, looking at a newspaper headline but not understanding what it’s saying. Both are important skills to help you function in the everyday. Without either one, doing everyday work gets a little harder. Knowing how to read a graph in science class is no different. Graph analysis is an important skill and, without it, learning science gets a little harder.

Unfortunately, students struggle with graph analysis and, specifically, interpolation. Recent results from REAL Science Challenge Vol 2 Contest 1 support this claim. In questions where students need to practice interpolation (ie. Finding a value for y given a value of x and vice versa), only x% of students provide the correct answer. That means x students in a class of 30 struggle in graph analysis, in finding values from a graph.

In this post, we provide a quick overview and some examples on how to examine a graph and get some values through interpolation. At the end of our post, we have a cheat sheet available for download.

## Why is graph analysis important?

Graph analysis is really about finding relevant information from a graph to solve a problem. Students need to know what information to extract from a graph before analysis can occur.

## I. Basic Line Graph Analysis

Consider the following line graph:

BEFORE STARTING: Check the axes and their values.

### If given a value that is plot along x-axis:

1. Find given value along x axis.
2. From this point, trace a straight line vertically (parallel to the y-axis) until it intersects with the line graph.
3. Then, trace a line horizontally (parallel to the x axis) from the intersect to the y-axis.
4. The value of y corresponding to the given x value is where the traced line intercepts with the y-axis.

For example, consider we want to determine the cost of installing a fence that is 17 feet in length.

Through graph interpolation, we can estimate that the cost would be roughly \$410.

### If given a value plot along the y axis:

1. Find given value along y axis.
2. From this point, trace a straight line horizontally (parallel to the x-axis) until it intersects with the line graph.
3. Then, trace a line vertically (parallel to the y axis) from the intersect to the x-axis.
4. The value of x corresponding to given y value is where the traced line intercepts with the x axis.

For example, consider we want to determine what length fence we can install for \$275.

Through graph interpolation, we can determine that the fence would be 8 feet in length.

## II. Basic Bar Graph Analysis

Consider the following bar graph.

The steps for bar graph analysis are similar to those for a line graph. However, since individual bars on a bar graph represent the range of possible values for a given x or y condition, a bar can potentially intersect with a range of x or y conditions. Thus, interpolating bar graphs can produce multiple results (unlike most line graphs that typically produce a single result).

For example, let’s say we want to determine what fiction books had \$60 million of gross earnings.

1. We find given value along y axis. From this point, trace a straight line horizontally (parallel to the x-axis) until it intersects with the bar graphs.
2. Then, trace line(s) vertically (parallel to the y axis) from the intersect(s) to the x-axis.

Through graph interpolation, we find multiple values that match the original query (romance novels from 2006-2010 and mystery novels from 2006-2007).

## Wrap Up

Learning to read a graph is an important skill every student needs to learn how to do properly. Being able to extract data is the first step towards analyzing data, and teachers need to teach it explicitly. And, students need to practice the skill too (REAL Science examples to follow in a future post). Click the link below to download our REAL Science – Interpolation Cheat Sheet.

Until next time, keep it REAL.

Posted on January 9, 2018 in Strategies