Interpolation involves using the values of the data to calculate a number between them. This can be done graphically or with an equation. It is important to know how to interpolate numbers because it can help you better understand the data by trying to determine the values of the data that were not specifically given in the initial set. You only need a few sets of values in order to interpolate.

### Step 1

Make a table of the data values, then create a graph from those values. For example, you may be given data about the number of students that failed the math placement exam for the years 2000, 2002, 2004, and 2006. In the year 2000, 100 students failed. In 2002, 90 students failed. In 2004, 48 students failed. In 2006, 32 students failed. The problem may ask you to use interpolation to find the number of students who failed the test in the 2001.

### Step 2

Make a graph of the data in the table. Put the years on the x-axis and the number of students that failed on the y-axis. Connect all of the points with a line.

### Step 3

Use a ruler to make a vertical line from the x value of 2001 to the line of the graph. Make a horizontal line from the point on the graph, to the y-axis. Doing this graphical interpolation, you may find that about 95 students failed the math placement test in the year 2001.

### Step 4

Know the formula for the linear interpolation process. The formula is

y = y1 + ((x - x1) / (x2 - x1)) * (y2 - y1), where x is the known value, y is the unknown value, x1 and y1 are the coordinates that are below the known x value, and x2 and y2 are the coordinates that are above the x value.

### Step 5

Write down the numbers that you are going to put into the equation. Since your unknown x value is the year 2001, you will use the values in the table for 2000 and 2002. Therefore, x = 2001, x1 = 2000, y1 = 100, x2 = 2002, and y2 = 90.

### Step 6

Put the values of the data into the linear interpolation formula. For example, you have

y = 100 + ((2001 - 2000) / (2002 - 2000)) x (90 - 100). You should receive an answer of 95 students. Therefore, in the year 2001, 95 students failed the math placement exam.